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RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3

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RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3

Other Exercises

Question 1.
A bucket has top and bottom diameters of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of ?1.20 per dm2. (Use % = 3.14)
Solution:
Upper diameter = 40 cm
and lower diameter = 20 cm
∴  Upper radius (r1) = \((\frac { 40 }{ 2 } )\) = 20 cm
and lower radius (r2) = \((\frac { 20 }{ 2 } )\) = 10 cm
Depth or height (h) = 12 cm
Volume of the bucket
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 1

Question 2.
A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
Solution:
Base diameter of frustum = 20 cm 20
∴  Radius (r1) = \((\frac { 20 }{ 2 } )\) = 10 cm
and diameter of top = 12 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 2

Question 3.
The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface of the frustum.
Solution:
Perimeter of the top of frustum = 18 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 3

Question 4.
The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.
Solution:
Perimeter of the top of frustum = 44 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 4
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 5
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 6

Question 5.
If the radii of the circular ends of a conical bucket which is 45 cm high be 28 cm and 7 cm, find the capacity of the bucket. (Use π = 22/7). (C.B.S.E. 2000)
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 7

Question 6.
The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be \((\frac { 1 }{ 125 } )\)  of the volume of the original cone, determine at what height above the base the section is made.
Solution:
Total height of the cone (h1) = 20 cm
Let a cone whose height is h2 is cut off Then height of the remaining portion (frustum)
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 8
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 9

Question 7.
If the radii of the circular ends of a bucket 24 cm high are 5 cm and 15 cm respectively, find the surface area of the bucket.
Solution:
Height of the bucket (frustum) (A) = 24 cm
Radius of the top (r1) = 15 cm 1
and radius of the bottom (r2) = 5 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 10

Question 8.
The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.
Solution:
Height of the frustum (A) = 12 cm
Radius of the top (r1) = 12 cm
and radius of the bottom (r2) = 3 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 11

Question 9.
A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m, the height of the frutum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)
Solution:
Radius of the bottom of the tent (r1) = 13 m
and radius of the top (r2) = 7 m
Height of frustum portion (h1) = 8 m
Slant height of the conical cap (l2) = 12 m
Let l1 be the slant height of the frustum portion, then
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 12

Question 10.
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹44 per litre which the container can hold. [NCERT Exemplar]
Solution:
Given that, height of milk container (h) = 16 cm
Radius of lower end of milk container (r) = 8 cm
and radius of upper end of milk container (R) = 20 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 13
∴ Volume of the milk container made of metal sheet in the form of a frustum of a cone
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 14

Question 11.
A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the bucket. Also, find the cost of milk which can completely fill the container, at the rate of ₹25 per litre. (Use π = 3.14) [NCERT Exemplar]
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 15

Question 12.
A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm³ of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use π = 3.14). [CBSE 2006C]
Solution:
Volume of frustum (bucket) = 12308.8 cm³
Upper radius (r1) = 20 cm
and lower radius (r2) = 12 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 16
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 17

Question 13.
A bucket made of aluminium sheet is of height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs. 70 per 100 cm². (Use π = 3.14) (C.B.S.E. 2006C)
Solution:
Height of bucket (frustum) (h) = 20 cm
Upper radius (r1) = 25 cm
and lower radius (r2) = 10
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 18

Question 14.
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. (C.B.S.E. 2005)
Solution:
Upper radius of frustum (r1) = 3.3 cm
and lower radius (r2) = 27 cm
Slant height (l) = 10 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 19

Question 15.
A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used is Rs. 20 per 100 cm². (Use π = 3.14) (CBSE 2008)
Solution:
Lower radius of bucket (r) = \((\frac { 16 }{ 2 } )\) = 8 cm
and upper radius (R) = \((\frac { 40 }{ 2 } )\) = 20 cm
Height (h) = 16
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 20

Question 16.
A solid is in the shape of a frustum of a cone. The diameter of the two circular ends are 60 cm and 36 cm and the leight is 9 ³cm. Find the area of its whole surface and the volume. [CBSE 2010]
Solution:
In a solid frustum upper diameter = 60 cm
∴ Radius (r1) = \((\frac { 60 }{ 2 } )\) = 30 cm
Lower diameter = 36 cm 36
∴ Radius (r2) = \((\frac { 36 }{ 2 } )\) = 18 cm
Height (h) = 9 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 21

Question 17.
A milk container is made of metal sheet in the shape of frustum of a cone whose volucrn is 10459\((\frac { 3 }{ 7 } )\) cm³. The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs. 1.40 per cm². (Use π = 22.7) [CBSE 2010]
Solution:
Volume of frustum = 10459\((\frac { 3 }{ 7 } )\) cm3 73216
= \((\frac { 73216 }{ 7 } )\) cm³
Lower radius (r2) = 8 cm
and upper radius (r1) = 20 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 22
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 23

Question 18.
A solid cone of base radius 10 cm is cut into two parts through the mid-pint of its height, by a plane parallel to its base. Find the ratio in the volumes of two parts of the cone. [CBSE 2013]
Solution:
Radius of solid cone (r) = 10 cm
Let total height = h
In ΔAOB,
C is mid point of AO and CD || OB
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 24

Question 19.
A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of ₹10 per 100 cm². (Use π = 3.14). [CBSE 2013]
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 25

Question 20.
In the given figure, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use π = 22/7 and \(\sqrt { 5 } \) = 2.236).  [ CBSE 2015]
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 26
Solution:
Total height of cone = 12 cm
Radius of its base = 6 cm
A cone of height 4 cm is cut out
Height of the so formed frustum = 12 – 4 = 8 cm
Let r be the radius of the cone cut out
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 27

Question 21.
The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.
Solution:
Let the height and radius of the given cone be H and R respectively.
The cone is divided into two parts by drawing a plane through the mid point of its axis and parallel to the base.
Upper part is a smaller cone and the bottom part is the frustum of the cone.
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 28
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 29

Question 22.
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at ₹40 per litre, find the amount received by the person. [CBSE 2017]
Solution:
Radii of the bucket in the form of frustum of cone = 30 cm
and 12 cm Depth of the bucket = 35 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 30

Question 23.
A reservoir in the form of the frustum of a right circular cone contains 44 x 107 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take : π = 22/7)
Solution:
A reservoir is a frustum in shape and its upper radius (r1) = 100 m
Lower radius (r2) = 50 m
and capacity of water in it = 44 x 107 litres
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 31
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 32

P.Q. A metallic right circular cone 20 cm high and whose vertical angle is 90° is cut into two parts at the middle point of its axis by a plane parallel to the base. If the frustum so obtained be drawn into a wire  \((\frac { 1 }{ 16 } )\)cm, find the length of the wire.

Solution: In the cone ABC, ∠A = 90°, AL ⊥ BC and = 20 cm
It is cut into two parts at the middle point M on the axis AL
AL bisects ∠A also
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 33
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3 34

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CA Foundation Business Economics Study Material – Law of Demand

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CA Foundation Business Economics Study Material Chapter 2 Theory of Demand and Supply – Law of Demand

The Law of Demand

  • The Law of Demand expresses the nature of functional relationship between the price of a commodity and its quantity demanded.
  • It simply states that demand varies inversely to the changes in price i.e. demand for a commodity expands when price falls and contracts when price rises.
  • “Law of Demand states that people will buy more at lower prices and buy less at higher prices, other things remaining the same.” (Prof. Samuelson)
  • It is assumed that other determinants of demand are constant and ONLY PRICE IS THE VARIABLE AND INFLUENCING FACTOR.
  • Thus, the law of demand is based on the following main assumptions:—
    1. Consumers income remain unchanged.
    2. Tastes and preferences of consumers remain unchanged.
    3. Price of substitute goods and complement goods remain unchanged.
    4. There are no expectations of future changes in the price of the commodity.
    5. There is no change in the fashion of the commodity etc.
  • The law can be explained with the help of a demand schedule and a corresponding demand curve.
  • Demand schedule is a table or a chart which shows the different quantities of commodity demanded at different prices in a given period of time.
  • Demand schedule can be Individual Demand Schedule or Market Demand Schedule.

Individual Demand Schedule is a table showing different quantities of commodity that ONE PARTICULAR CONSUMER is willing to buy at different level of prices, during a given period of time.

ca-foundation-business-economics-study-material-law-of-demand

Market Demand Schedule is a table showing different quantities of a commodity that ALL THE CONSUMERS are willing to buy at different prices, during a given period of time.

ca-foundation-business-economics-study-material-law-of-demand-1
(Assumption: There are only 2 buyers in the market)

Both individual and market schedules denotes an INVERSE functional relationship between price and quantity demanded. In other words, when price rises demand tends to fall and vice versa.

A demand curve is a graphical representation of a demand schedule or demand function.

  • A demand curve for any commodity can be drawn by plotting each combination of price and demand on a graph.
  • Price (independent variable) is taken on the Y-axis and quantity demanded (dependent variable) on the X-axis.

ca-foundation-business-economics-study-material-law-of-demand-2

  • Individual Demand Curve as well as Market Demand Curve slope downward from left to right indicating an inverse relationship between own price of the commodity and its quantity demanded.
  • Market Demand Curve is flatter than individual Demand Curve.

Reasons for the law of demand and downward slope of a demand curve are as follows:—

1. The Law of Diminishing Marginal Utility:

  • According to this law, other things being equal as we consume a commodity, the marginal utility derived from its successive units go on falling.
  • Hence, the consumer purchases more units only at a lower price.
  • A consumer goes on purchasing a commodity till the marginal utility of the commodity is greater than its market price and stops when MU = Price ie. when consumer is at equilibrium.
  • When the price of the commodity falls, MU of the commodity becomes greater than price and so consumer start purchasing more till again MU = Price.
  • It therefore, follows that the diminishing marginal utility implies downward sloping demand curve and the law of demand operates.

2. Change in the number of consumers:

  • Many consumers who were unable to buy a commodity at higher price also start buying when the price of the commodity falls.
  • Old customers starts buying more when price falls.

3. Various uses of a commodity:

  • Commodity may have many uses. The number of uses to which the commodity can be put will increase at a lower price and vice versa.

4. Income effect:

  • When price of a commodity falls, the purchasing power (ie. the real income) of the consumer increases.
  • Thus he can purchase the same quantity with lesser money or he can get more quantity for the same money.
  • This is called income effect of the change in price of the commodity.

5. Substitution effect:

  • When price of a commodity falls it becomes relatively cheaper than other commodities.
  • As a result the consumer would like to substitute it for other commodities which have now become more expensive.
    E.g. With the fall in price of tea, coffee’s price remaining the same, tea will be substituted for coffee.
  • This is called substitution effect of the change in price of the commodity.
  • Thus, PRICE EFFECT = INCOME EFFECT + SUBSTITUTION EFFECT as explained by Hicks and Allen.

Exceptions to the Law of Demand

  • Law of Demand expresses the inverse relationship between price and quantity demanded of a commodity. It is generally valid in most of the situations.
  • But, there are some situations under which there may be direct relationship between price and quantity demanded of a commodity.

These are known as exceptions to the law of demand and are as follows:—

1. Giffen Goods:

  • In some cases, demand for a commodity falls when its price fall and vice versa.
  • In case of inferior goods like jawar, bajra, cheap bread, etc. also called “Giffen Goods” (known after its discoverer Sir Robert Giffens) demand is of this nature.
  • When the price of such inferior goods fall, less quantity is purchased due consumer’s increased preference for superior commodity with the rise in their “real income” (Le. purchasing power).
  • Hence, other things being equal, if price of a Giffen good fall its demand also falls.
  • There is positive price effect in this case.

2. Conspicuous goods:

  • Some consumers measure utility of a commodity by its price i.e. if the commodity is expensive they think it has got more utility and vice versa.
  • Therefore, they buy less at lower price and more of it at higher price.
    E.g. Diamonds, fancy cars, dinning at 5 stars, high priced shoes, ties, etc….
  • Higher prices are indicators of higher utilities.
  • A higher price means higher prestige value and higher appeal and vice versa.
  • Thus a fall in their price would lead to fall in their quantities demanded. This is against the law of demand.
  • This was found out by Veblen in his doctrine of “Conspicuous Consumption” and hence this effect is called Vebleri effect or prestige effect.

3. Conspicuous necessities:

  • The demand for some goods is guided by the demonstration effect of the consumption pattern of a social group to which the person belongs.
    E.g. Television sets, refrigerators, music systems, cars, fancy clothes, washing machines etc.
  • Such goods are used just to demonstrate that the person is not inferior to others in group.
  • Hence, inspite of the fact that prices have been continuously rising, their demand does not show tendency to fall.

4. Future changes in prices:

  • When the prices are rising, households tend to purchase larger quantities of the commodity, out of fear that prices may go up further and vice versa.
    E.g. – Shares of a good company, etc.

5. Irrational behaviour of the consumers:

  • At times consumers make IMPULSIVE PURCHASES without any calculation about price and usefulness of the product. In such cases the law of demand fails.

6. Ignorance effect:

  • Many times households may demand larger quantity of a commodity even at a higher price because of ignorance about the ruling price of the commodity in the market.

7. Consumer’s illusion:

  • Many consumers have a wrong illusion that the quality of the commodity also changes with the price change.
  • A consumer may contract his demand with a fall in price and vice versa.

8. Demand for necessaries:

  • The law of demand does not hold true in case of commodities which are necessities of life. Whatever may be the price changes, people have to consume the minimum quantities of necessary commodities. E.g.- rice, wheat, clothes, medicines, etc.

DEMAND CURVE FOR ABOVE EXCEPTIONS IS POSITIVELY SLOPED

Expansion and Contraction of Demand

(changes in quantity demanded. Or movement along a demand curve)

  • The law of demand, the demand schedule and the demand curve all show that
    – when the price of a commodity falls its quantity demanded rises or expansion takes place and
    – when the price of a commodity rises its quantity demanded fall or contraction takes place.
  • Thus, expansion and contraction of demand means changes in quantity demanded due to change in the price of the commodity other determinants like income, tastes, etc. remaining constant or unchanged.
  • When price of a commodity falls, its quantity demanded rises. This is called expansion of demand.
  • When price of a commodity rises, its quantity demanded falls. This is called contraction of demand.
  • As other determinants of price like income, tastes, price of related goods etc. are constant, the position of the demand curve remains the same. The consumer will move upwards or downwards on the same demand curve.

ca-foundation-business-economics-study-material-law-of-demand-3
Figure : Expansion and Contraction of Demand

In the figure

  • At price OP quantity demanded is OQ.
  • With a fall in price to OP1, the quantity demanded rises from OQ toOQ1,. The coordinate point moves down from E to E1This is called ‘expansion of demand’ or ‘a rise in quantity demanded’ or ‘downward movement on the same demand curve’.
  • At price OP quantity demanded is OQ.
  • With a rise in price to P2, the quantity demanded falls from OQ to OQ2. The coordinate point moves up from E to E2. This is called ‘contraction of demand’ or ‘a fall in quantity demanded’ or ‘upward movement on the same demand curve’.
  • Thus, the downward movement on demand curve is known as expansion in demand and an upward movement on demand curve is known as contraction of demand.

Increase and Decrease in demand (changes in demand OR shift in demand curve)

  • When there is change in demand due to change in factors other than price of the commodity, it is called increase or decrease in demand.
  • It is the result of change in consumer’s income, tastes and preferences, changes in population, changes in the distribution of income, etc.
  • Thus, price remaining the same when demand rises due to change in factors other than price, it is called increase in demand. Here, more quantity is purchased at same price or same quantity is purchased at higher price.
  • Likewise price remaining the same when demand falls due to change in factors other than price, it is called decrease in demand. Here, less quantity is purchased at same price or same quantity is purchased at lower price.
  • In above cases demand curve shifts from its original position to rightward when demand increases and to leftward when demand decreases. Thus, change in demand curve as a result of increase or decrease in demand, is technically called shift in demand curve.

ca-foundation-business-economics-study-material-law-of-demand-4
Figure : Increase and Decrease in Demand

In the figure

  • Original demand curve is DD. At OP price OQ quantity is being demanded.
  • As the demand changes, the demand curve shifts either to the right (D1D1) or to the left (D2D2)
  • At D1D1, OQ1, quantity is being demanded at the price OP. This shows increase in demand (rightward shifts in demand curve) due to factor other than price.
  • At D2D2, QO2 quantity is being demanded at the price OP. This shows decrease in demand (leftward shift in demand curve) due to a factor other than price.
  • When demand of a commodity INCREASES due to factors other than price, firms can sell a larger quantity at the prevailing price and earn higher revenue.
  • The aim of a advertisement and sales promotion activities is to shift the demand curve to the right and to reduce the elasticity of demand.

 

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2

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RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2

Other Exercises

Question 1.
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.
Solution:
Diameter of the base of the tent = 24 m
∴ Radius (r)= \((\frac { 24 }{ 2 } )\)  = 12m
Total height of the tent = 16 m
Height of the cylindrical portion (h1) = 11 m
Height of the conical portion (h2) =16-11 = 5 m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 1

Question 2.
A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius 2.5 m and height 21 m and the cone has the slant height 8 m. Calculate the total surface area and the volume of the rocket.
Solution:
Radius of the base of the rocket (r) = 2.5 m
Height of cylindrical portion (h1) = 21 m
Slant height of the conical portion (l) = 8 m
Let height of conical portion = h2
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 2
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 3

Question 3.
A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44
dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m2 . (Use π = 22/7).
Solution:
Total height of the tent = 77 dm
Height of cylindrical part (h1) = 44 dm
= 4.4 m
Height of conical part (h2) = 7.7 – 4.4 = 3.3 m
Diameter of the base of the tent = 36 m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 4
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 5

Question 4.
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy. (Use π = 3.14).
Solution:
Diameter of the base of the toy = 6 cm
∴ Radius (r) = \((\frac { 6 }{ 2 } )\)  = 3 cm
Height (h) = 4 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 6
Total surface area of the toy = curved surface area of the conical part + surface area of the hemispherical part
= πrl + 2πr² = πr (l + 2r)
= 3.14 x 3 (5 + 6) = 3.14 x 3 x 11 cm²
= 3.14 x 33 = 103.62 cm²

Question 5.
A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the ~ heights of the cylindrical and conical portions are 10 cm and 6 cm, respectively. Find the total surface area of the solid. (Use π = 22/7)
Solution:
Radius of the common base (r) = 3.5 m
Height of cylindrical part (h1) = 10 cm
Height of conical part (h2) = 6 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 7
Now total surface area of the solid = curved surface of conical part + curved surface of cylindrical part + curved surface of hemispherical part
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 8

Question 6.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm. (C.B.S.E. 2002)
Solution:
Radius of the base of the cylindrical part (r) = 5 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 9
Height of cylindrical part (h1) = 13 cm
Height of the conical part (h2) = 30 – (13 + 5) = 30- 18 = 12 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 10

Question 7.
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub. (Take π = 22/7) (C.B.S.E. 2000C)
Solution:
Radius of the cylindrical tub (R) = 5 cm
and height (h1) = 9.8 cm
Radius of the solid (r) = 3.5 cm
and height of cone (h1) = 5 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 11
= 38.5 x 4 = 154 cm3
∴ Water flowed out of the tub = 154 cm³
Remaining water in the tub = 770 – 154
= 616 cm³

Question 8.
A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20 m. The heights of the cylindrical and conical portions are 4.2 m and 2.1 m respectively. Find the volume of the tent.
Solution:
Radius of the tent (r) = 20 m
Height of the conical part (h1) = 2.1 m
and height of the cylindrical part (h2) = 4.2 m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 12

Question 9.
A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm. Determine the capacity of the tank.
Solution:
Diameter of cylindrical part = 21 cm 21
∴ Radius (r) = \((\frac { 21 }{ 2 } )\) cm
Height of cylindrical part (h1) = 18 cm
and height of each conical part (h2) = 9 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 13

Question 10.
A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.
Solution:
Base radius of the cylinder (r) = 5 cm
and height (h) = 12 cm
∴ Volume = πr2h = n (5)2 x 12 cm3 = 300π cm3
∵ The base and height of the cone drilled are the same as those of the cylinder
∴ Volume of cone = \((\frac { 1 }{ 3 } )\)πr2h
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 14

Question 11.
A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs. 100 per square metre.
Solution:
Diameter of the base of the tent = 20 m
∴ Radius (r) =\((\frac { 20 }{ 2 } )\) = 10 m
Height of cylindrical part (h1) = 2.5 m
and height of conical part (h2) = 7.5 m
Slant height of the conical part (l)
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 15
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 16

Question 12.
A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.
Solution:
Diameter of the cylinder = 2 m
∴ Radius (r) = \((\frac { 1 }{ 3 } )\) = 1 m
Height (length) of cylindrical part (h) = 2 m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 17

Question 13.
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is \((\frac { 14 }{ 3 } )\) m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.
Solution:
Diameter of the cylindrical part = 3.5 m
∴Radius (r) = \((\frac { 3.5 }{ 2 } )\) = 1.75 = \((\frac { 7 }{ 4 } )\) m
and height (h) = \((\frac { 14 }{ 3 } )\) m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 18
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 19

Question 14.
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs. 10 per dm2 . (C.B.S.E. 2006C)
Solution:
Total height = 104 cm
Radius of hemispherical part (r) = 7 cm
Height of cylinder (h) = 104 cm – 2 x 7 cm = 104- 14 = 90 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 20
Total outer surface area = curved surface area of the cylindrical part + 2 x curved surface area of each hemispherical part
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 21

Question 15.
A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic centimeters of cork dust will be required ?
Solution:
Diameter of inner cylinder = 14 cm
∴Radius (r) = \((\frac { 14 }{ 2 } )\) = 7 cm
Diameter of outer cylinder = 16 cm
∴ Radius (R) = \((\frac { 16 }{ 2 } )\) = 8 cm
Height (h) = 42cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 22

Question 16.
A cylindrical road roller made of iron is 1 m long. Its internal diameter is 54 cm and the thickness of the iron sheet used in making the roller is 9 cm. Find the mass of the roller, if 1 cm³ of iron has 7.8 gm mass. (Use π = 3.14)
Solution:
Length of roller (h) = 1 m = 100 cm
Inner diameter = 54 cm
Thickness of iron sheet = 9 cm
∴ Inner radius (r) = \((\frac { 52 }{ 2 } )\) = 27 cm
and outer radus (R) = 27 + 9 = 36 cm
∴ Volume of the mass = πR²h – πr²h
= πh (R²- r²)
= 3.14 x 100 (36² – 27²) cm3
= 314 x (36 + 27) (36- 27) cm3
= 314 x 63 x 9 cmc
= 178038 cm3
Weight of 1 cm3 of iron = 7.8 gm
∴ Total weight = 178038 x 7.8 gm
= 1388696.4 gm
= 1388.6964 kg
= 1388.7 kg

Question 17.
A vessel in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Solution:
Diameter of hemisphere = 14 cm
Total height =13 cm
Radius of hemisphere = \((\frac { 14 }{ 2 } )\) = 7 cm
∴ Height of cylindrical part =13-7 = 6 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 23
∴  Inner surface area of the vessel = inner surface area of cylindrical part + inner surface area of hemispherical part
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 24

Question 18.
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Solution:
Radius of cone (r) – 3.5 cm
Total height of the toy = 15.5 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 25
Height of the conical part (h) = 15.5 – 3.5 = 12 cm
∴ Slant height of the cone (l)
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 26

Question 19.
The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.
Solution:
In cylindrical metallic pipe,
length of pipe = 14 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 27
Difference between outside and inside
surface area = 44 m2
Volume of pipe material = 99 cm3
Let R and r be the outer and inner radii of the pipe respectively, then Outer surface area – inner surface area = 44 cm2
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 28

Question 20.
A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Solution:
Height of cylinder (H) = 15 cm
and diameter =12 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 29
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 30

Question 21.
A solid iron pole having cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that the mass of 1 cm3 of iron is 8 gm.
Solution:
Diamter of the base = 12 cm
∴ Radius (r) = \((\frac { 12 }{ 2 } )\) = 6 cm
Height of the cylindrical portion (h1)= 110 cm
and height of conical portion (h2) = 9 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 31
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 32

Question 22.
A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.
Solution:
Height of conical part (h) = 2 cm
Diameter of base = 4 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 33
Now volume of the cylinder which circum scribes the toy = πr²h
= π (2)² x 4 = 16π cm³
∴  Difference of their volumes = 16π – 8π = 8πcm³

Question 23.
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Solution:
Radius of conical part = 60 cm
and height (h) = 120 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 34
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 35

Question 24.
A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder. (ii) left in the cylinder. (C.B.S.E. 2009)
Solution:
Internal diameters of cylindrical vessel = 10 cm
∴ Radius (r) = \((\frac { 10 }{ 2 } )\) =5 cm
and height (h) = 10.5 cm
∴ Volume of water filled in it
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 36

Question 25.
A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block. [CBSE 2010]
Solution:
Edge of cube = 21 cm
∴ Diameter of the hemisphere curved out of
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 37

Question 26.
A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy. (Use π = 22/7).
Solution:
Radius of base of the conical part (r) = 21 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 38
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 39

Question 27.
A solid is in the shape of a cone surmounted on a hemi-sphere, the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. [CBSE 2012]
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 40
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 41

Question 28.
An wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius
3.5 cm, find the volume of wood in the toy. (Use π = 22/7). [CBSE 2013]
Solution:
Height of cylindrical part (h) = 10 cm
Radius of the base (r) = 3.5 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 42

Question 29.
The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. (Use π = 22/7). [CBSE 2014]
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 43

Question 30.
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid, (take π = 22/7). [CBSE 2014]
Solution:
Diameter of solid cylinder= 4.2 cm
∴ Radius (r) =\((\frac { 4.2 }{ 2 } )\) = 2.1 cm
Height (h) = 2.8 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 44

Question 31.
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid. [CBSE 2015]
Solution:
Side of a solid cube (a) = 21 cm
∴ Volume = a3, = (21 )3 cm3
= 9261 cm3
Diameter of the base of cone = 21 cm
Now radius of cone curved from it (r) =\((\frac { 21 }{ 2 } )\) cm
and height (h) = 21 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 45

Question 32.
A solid wooden toy is in the form of a hemisphere surmounted by a Cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 \((\frac { 5 }{ 6 } )\) cm3 . Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of ₹10 per cm2. (Take π  = 22/7). [CBSE 2015]
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 46
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 47

Question 33.
In the given figure, from a cuboidal solid metalic block, of dimensions 15 cm x 10 cm x 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block. (Take  π = 22/7) [CBSE 2015]
Solution:
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 48
Radius of hole = \((\frac { 7 }{ 2 } )\)cm and height = 5 cm
Length of block (l) = 15 cm
Breadth (b) = 10 cm and height = 5 cm
∴ Surface area = 2(lb + bh + hl)
= 2(15 x 10 + 10 x 5 + 5 x 15) cm2
= 2(150 + 50 + 75) = 2 x 275 = 550 cm2
Area of circular holes of both sides = 2 x πr2
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 49

Question 34.
 A building is in the form of a cylinder surmounted by a hemi-spherical vaulted dome and
contains 41 \((\frac { 19 }{ 21 } )\) m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building? [NCERT Exemplar]
Solution:
Let total height of the building = Internal diameter of the dome = 2rm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 50
Radius of building (or dome) = \((\frac { 2r }{ 2 } )\) = r m
Height of cylinder = 2r-r = rm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 51

Question 35.
A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm x 5 cm x 4 cm. The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand. [NCERT Exemplar]
Solution:
Given that, length of cuboid pen stand (l) = 10 cm
Breadth of cuboid pen stand (b) = 5 cm
and height of cuboid pen stand (h) = 4 cm
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 52
∴ Volume of cuboid pend stand = l x b x h= 10 x 5 x 4 = 200 cm3
Also, radius of conical depression (r) = 0.5 cm
and height (depth) of a conical depression (h1) = 2.1 cm
∴ Volume of a conical depression = πrh1
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 53

Question 36.
 A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to \((\frac { 2 }{ 3 } )\) of the total height of the building. Find the height of the building, if it contains 67 \((\frac { 1 }{ 21 } )\) m3 of air.
Solution:
Let the radius of the hemispherical dome be r metres and the total height of the building be h metres.
Since the base diameter of the dome is equal to \((\frac { 2 }{ 3 } )\) of the total height, therefore
2 r = \((\frac { 2 }{ 3 } )\)h. This implies r = \((\frac { h }{ 3 } )\). Let H metres be the height of the cylindrical portion.
Therefore, H = h – \((\frac { h }{ 3 } )\) = \((\frac { 2 }{ 3 } )\)h metres.
Volume of the air inside the building = Volume of air inside the dome + Volume of the air inside the
cylinder = \((\frac { 2 }{ 3 } )\) πr3 + πr2H, where H is the height of the cylindrical portion
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 54

Question 37.
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of cone is 4 cm and the diameter of the base is 8 cm. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy. [NCERT Exemplar]
Solution:
Let r be the radius of the hemisphere and the cone and h be the height of the cone.
Volume of the toy=Volume of the hemisphere + Volume of the cone
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 55

= \((\frac { 1408 }{ 7 } )\) cm3
A cube circumsrcibes the given solid. Therefore, edge of the cube should be 8 cm. Volume of the cube = 83 cm3 = 512 cm3 Difference in the volume of the cube and
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 56

Question 38.
A circus tent is in the shape of a cylinder surmounted by a conical top of same diameter. If their common diameter is 56 m, the height of the cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of the canvas used in making the tent. [ICBSE 2017]
Solution:
We have, diameter of base of cylinder = d = 56 m
Radius of base of cylinder = r=  \((\frac { d }{ 2 } )\)=  \((\frac { 52 }{ 2 } )\)= 28 m
Height of tent = 27 m
Height of cylinder = 6 m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 57
Height of conical portion = 27 – 6 = 21 m
Radius of conical portion, r = 28 m
RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 58

Hope given RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 are helpful to complete your math homework.

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CA Foundation Business Economics Study Material – Introduction to Demand

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CA Foundation Business Economics Study Material Chapter 2 Theory of Demand and Supply – Introduction to Demand

Meaning of Demand

  • In ordinary speech, the term demand is many times confused with ‘desire’ or ‘want’.
  • Desire is only a wish to have any thing.
  • In economics demand means more than mere desire.
  • Demand in economics means an effective desire for a commodity ie. desire backed by the ‘ability to pay’ and ‘willingness to pay’ for it.
  • Thus, demand refers to the quantity of a good or service that consumers are willing and able to purchase at different prices during a period of time.
  • Thus, defined, the term demand shows the following features:
    1. Demand is always with reference to a PRICE.
    2. Demand is to be referred to IN A GIVEN PERIOD OF TIME.
    3. Consumer must have the necessary purchasing power to back his desire for the commodity.
    4. Consumer must also be ready to exchange his money for the commodity he desires.
  • E.g. Mr. A’s demand for sugar at Rs. 15 per kg. is 4 kgs. per week.

Determinants of Demand

For estimating market demand for its products, a firm must have knowledge about—
(a) the determinants of demand for its product, and
(b) the nature of relationship between demand and is determinants.

The various factors on which the demand for a product/commodity depends are as follows:—

Price of the commodity:

  1. Other things being equal, the demand for a commodity is inversely related with its price.
  2. It means that a rise in price of a commodity brings about fall in its demand and vice versa.
  3. This happens because of income and substitution effects.

Price of the related commodities:

  1. The demand for a commodity also depends on the prices of related commodities.
  2. Related commodities are of two types namely—
    • Substitutes or competitive goods, &
    • Complementary goods.
  3. Substitute goods are those goods which can be used with equal ease in place of one another.
  4. E.g. Essar Speed Card and Airtel Magic Card; Coke and Pepsi; ball pen and ink pen; tea and coffee; etc.
  5. Demand for a particular commodity is affected if the price of its substitute falls or rises.
  6. E.g. If the price of Airtel Magic card falls, its demand will increase and demand for Essar Speed Card would fall and vice versa.
  7. Thus, there is a POSITIVE RELATIONSHIP between price of a commodity and demand for its substitutes.
  8. Complementary good are those goods whose utility depends upon the availability of both the goods as both are to be used together.
  9. E.g. a ball pen and refill; car and petrol; a hand set and phone connection; a tonga and horse, etc.
  10. The demand for complementary goods have an INVERSE RELATIONSHIP with the price of related goods.
  11. E.g. If the price of Scooters falls, its demand will increase leading to increase in demand for petrol.

Income of the consumers

  1. Other things being equal, generally the quantity demanded of a commodity bear a DIRECT RELATIONSHIP to the income of the consumer ie. with an increase in income, the demand for a commodity rises.
  2. However, this may not always hold true. It depends upon the class to which commodity belongs ie. necessaries or comforts and luxuries or inferior goods:
    • Necessaries (E.g. Food, clothing and shelter). Initially, with an increase in the in-come, the demand for necessaries also rises upto some limit. Beyond that limit, an increase in income will leave the demand unaffected.
    • Comforts and Luxurious (E.g. Car; Air-Conditioners; etc.) Quantity demanded of these group of commodities have a DIRECT RELATIONSHIP with the income of the consumers. As the income increases, the demand for comforts and luxuries also increases.
    • Inferior goods (E.g. Coarse grain; rough cloth; skimmed milk; etc.). Inferior goods are those goods for which superior substitutes are available Quantity demanded of this group of commodities Have an INVERSE RELATIONSHIP with the income of the consumer. E.g. A consumer starts consuming full cream milk (normal good) in place of toned milk (inferior good) with an increase in income.

Therefore, it is essential that business managers must know—

  • the nature of good they produce,
  • the nature of relationship between the quantities demanded and changes in consumer’s income, and
  • the factors that could bring about changes in the incomes of the consumers.

Tastes and Preferences of the consumers

  • Tastes and preferences of consumers generally change over time due to fashion, advertisements, habits, age, family composition, etc. Demand for a commodity bears a direct relationship to those determinants.
  • Modern goods or fashionable goods have more demand than the goods which are of old design and out of fashion.
    E.g. People are discarding Bajaj Scooter for say Activa Scooter.
  • The demand of certain goods is determined by ‘bandwagon effect’ or ‘demonstration effect’. It means a buyer wants to have a good because others have it. It means that an individual consumer’s demand is conditioned by the consumption of others.
  • Taste and preferences may also undergo a change when consumer discover that consumption of a good increases his PRESTIGE. E.g. Diamonds, fancy cars, etc.
  • A good loses its prestige when it becomes a commonly used good. This is called ‘snob effect’.
  • Status seeking rich people buy highly priced goods only. This form of ‘conspicuous consumption’ or ‘ostentatius consumption’ is called ‘VEBLEN EFFECT’ (named after American economist THORSTEIN VEBLEN)
  • Tastes and preferences of people change either due to external causes or internal causes.
  • Therefore, knowledge about tastes and preferences is important in production planning, designing new products and services to suit the changing tastes and preferences of the consumers.

Other Factors. Other things being equal demand for a commodity is also determined by the following factors:—

  1. Size and composition of Population:
    • Generally, larger the size of population of a country, more will be the demand of the commodities.
    • The composition of the population also determines the demand for various commodities.
      E.g. If the number of teenagers is large, the demand for trendy clothes, shoes, movies, etc. will be high.
  2. The level of National Income and its Distribution:
    • National Income is an important determinant of market demand. Higher the national income, higher will be the demand for normal goods and services.
    • If the income in a country is unevenly distributed, the demand for consumer goods will be less.
    • If the income is evenly distributed, there is higher demand for consumer goods.
  3. Sociological factors:
    • The household’s demand for goods also depends upon sociological factors like class, family background, education, marital status, age, locality, etc.
  4. Weather conditions:
    • Changes in weather conditions also influence household’s demand.
      E.g. – Extraordinary hot summer push up the demand for ice-creams, cold drinks, coolers etc.
  5. Advertisement:
    • A clever and continuous campaign and advertisement create a new type of demand.
      E.g. Toilet products like soaps, tooth pastes, creams etc.
  6. Government Policy:
    • The government’s taxation policy also affects the demand for commodities.
    • High tax on a commodity will lead to fall in the demand of the commodity.
  7. Expectation about future prices:
    • If consumers expect rise in the price of a commodity in near future, the current demand for the commodity will increase and vice versa,
  8. Trade Conditions:
    • If the country is passing through boom conditions, demand for most goods is more.
    • But during depression condition, the level of demand falls.
  9. Consumer-credit facility and interest rates:
    • If ample credit facilities with low rates of interest is available, there will be more demand specially of consumer durable goods like scooters, LCD /LED televisions, refrigerators, home theatre, etc.

Demand Function

Mathematical/symbolic statement of functional relationship between the demand for a product (the dependent variable) its determinants (the independent variables) is called demand function

Dx = f (Px, M, Ps ; Pc, T, A)

Where—
Dx= quantity demanded of product
Px = the price of the product
M = money income of the consumer
Ps = the price of its substitute
Pc = the price of its complementary goods
T = consumer’s tastes and preferences
A = advertising effect measured through the level of advertisement expenditure.

CA Foundation Business Economics Study Material – Basic Problems of an Economy and Role of Price Mechanism

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CA Foundation Business Economics Study Material Chapter 1 Nature and Scope of Business Economics – Basic Problems of an Economy and Role of Price Mechanism

Basic Problems of an Economy

  • We know that human wants are unlimited and resources are scarce.
  • The problem of scarcity of resources is not only faced by individuals but also by the society at large.
  • This gives rise to the problem of how to use scare resources so as to serve best the needs of the society.
  • This economic problem is to be dealt with in all the economic systems whether capitalist or socialist or mixed.
  • The central problems relating to allocation of resources are:
    • What to produce and how much to produce?
    • How to produce?
    • For whom to produce?
    • What provision should be made for economic growth?

What to produce and how much to produce?

  • An economy has millions commodities to produce.
  • It has to decide what commodities are to be produced and how much.
  • E.g. – To produce luxury goods or consumer goods, etc.
  • Here, the guiding principle is to allocate the resources in the production of goods in such a way that maximizes aggregate utility.

How to produce ?

  • There are many alternative techniques to produce a commodity. ‘
  • Choice has to be made between capital intensive technique or labour intensive technique of production.
  • The choice of technique will depend upon —
    • availability of various factors of production, &
    • the prices of factors of production.
  • Such techniques of production has to be adopted that makes best use of available resources.

For whom to produce?

  • Who will consume the goods and services that are produced in the economy?
  • Whether a few rich or many poor will consume?
  • Goods and services are produced for those people who can purchase them or pay for them.
  • Paying capacity depends upon income or purchasing power.

What provisions should be made for economic growth?

  • A society cannot afford to use all its scarce resources for current consumption only.
  • It has to provide for the future as well so that high economic growth can be achieved.

Therefore, an economy has to take decisions about rate of savings, investment, capital formation, etc.

Meaning of Economic System

An economic system comprises the totality of forms through which the day to day economic process is at work. It refers to the mode of production, exchange, distributions and the role which government play in economic activity. There are three types of economic systems Capitalism, Socialism and Mixed Economy ‘

CAPITALIST ECONOMY

  • Capitalistic economic systems is one in which all the means of production are privately owned.
  • The owners of property, wealth and capital are free to use them as they like in order to earn profits.
  • The central problems about what, how and for whom to produce are solved by the free play of market forces.

Characteristics of Capitalist Economy:

  • There is right to own and keep private property by individuals. People have a right to acquire, use, control, enjoy or dispose off it as they like.
  • There is right of inheritance ie. transfer of property of a person to his legal heirs after his death.
  • There is freedom of enterprise ie. everybody is free to engage in any type of economic activity he likes.
  • There is freedom of choice by consumers ie. consumer is free to spend his income on whatever goods or services he wants to buy and consume.
  • Entrepreneurs or producers in their productive activity are guided by their profit motive. Thus profit motive is the guiding force behind all the productive activity.
  • There is stiff competition among sellers or producers of similar goods. There is competition among all the participants in the market.
  • Price mechanism is an important feature of capitalist economy were the price is determined through the interaction of market forces of demand and supply.

Merits of Capitalist Economy:

  • Capitalism works through price mechanism and hence self regulating
  • In capitalism there is greater efficiency and incentive to work due to two motivating force namely private property and profit motive.
  • Faster economic growth is possible.
  • There is optimum allocation of productive resources of the economy.
  • There is high degree of operative efficiency.
  • Cost effective methods are employed in order to maximise profits.
  • Consumers are benefited as large range of quality goods at reasonable prices are available from which they makes the choice. This also results in higher standard of living.
  • In capitalism there is more innovations and technological progress and country benefits from research and development, growth of business talent, etc.
  • Fundamental rights like right to private property and right to freedom are preserved.
  • It leads to emergence of new entrepreneurial class who is willing to take risks.

Demerits of Capitalist Economy:

  • In capitalism there is vast economic inequality and social injustice which reduces the welfare of the society.
  • There is precedence of property rights over human rights.
  • Cut-throat competition and profit motive work against consumer welfare leading to exploitation of consumers.
  • There are wastage of resources due to duplication of work and cut-throat competition.
  • Income inequalities lead to differences in economic opportunities. This lead to rich becoming richer and poor becoming poorer.
  • There is exploitation of labour.
  • More of luxury goods and less of wage goods are produced leading to misallocation of resources. .
  • Unplanned production, economic instability in terms of over production, depression, unemployment, etc. are common in a capitalist economy.
  • Leads to creation of monopolies.
  • Ignores human welfare because main aim is profit.

SOCIALIST ECONOMY

The concept of socialism was given by Karl Marx and Frederic Engels in their work ‘The Communist Manifesto’ published is 1848. A socialist economy is also called as “Command Economy” or a “Centrally Planned Economy.”

  • In a socialist economy, all the property, wealth and capital is owned by State. There is no private property.
  • State organises all economic activities. It owns, controls and manages the production units; it distributes the goods among the consumers; it decides the size and direction of investment.
  • The state works for the welfare of the people and not for profit.

Characteristics of Socialist Economy:

  • There is collective ownership of means of production Le. all the important means of production are state owned.
  • It is a centrally planned economy. All the basic decisions relating to the working and the regulation of the economy are taken by central authority called planning commission.
    • Production and distribution of goods is ensured through planning on preferences deter-mined by the state. So freedom from hunger is guaranteed but, consumer’s sovereignty is restricted.
  • There is social welfare in place of profit motive. Those goods and services are given top priority which is in the interest of largest number of people.
    • Price policy is guided by the aims of social welfare than profit motive.
  • There is lack of competition because it avoid duplication of efforts and wastage of resources. Hence, competition is done away.
  • Socialism tries to ensure equitable distribution of income through equality of opportunities. Thus, right to work is guaranteed but choice of occupation is restricted.

Merits of Socialist Economy:

  • Social justice is maintained by equitable distribution of income and wealth and by providing equal opportunities to all.
  • Balanced economic development is possible. Central planning authority allocate resources according to the plans and priorities.
  • There are no class conflict and community develops a co-operative mentality.
  • Unemployment is minimized, business fluctuations are eliminated resulting in stability.
  • Right to work is ensured and minimum standard of living is maintained.
  • There is no exploitation of consumers and workers.
  • Wastage of resources are avoided due to planning resulting in better utilization of resources and maximum production.
  • Citizens feel secure as there is social security cover for them.
  • Demerits of Socialist Economy:
  • There is predominance of bureaucracy resulting in inefficiency and delays.
  • There is no freedom of individuals as it takes away basic rights also like right of private property.
  • Workers are not paid according to their personal efficiency and productivity. This acts as disincentive to work hard.
  • Prices are administered by the state.
  • State monopolies may be created and may become uncontrollable. This will be more dan¬gerous than monopolies under capitalism.
  • The consumers have no freedom of choice.

MIXED ECONOMY

Mixed economy combines the features of both capitalism and socialism. The concept is designed to incorporate best of both. The main characteristics/features are:—

  • There is co-existence of both private and public sector ie. economic resources are owned by individuals and state.
    • State open those enterprises which are in the interest of the’society as a whole.
    • Private sector moves to those enterprises which produce higher profit.
  • There is co-existence of free price mechanism and economic planning.
    • Price mechanism is however curtailed through measures like price control, administered prices etc.
    • Planning is done through incentives like concessions, subsidies, etc. and disincentives like high rate of taxes, strict licensing etc.
  • In mixed economy social welfare motive gets due importance particularly in case of poor and backward classes.
    Eg. Subsidised hospital, food articles, education etc.; social security schemes like old age pension, reservation of jobs, laws in the interest of workers, consumers, human, children etc.
  • There is freedom to joint any occupation, trade or service according to the education, training, skills and ability.
  • There is freedom of consumption. People are free to consume goods and services of their choice and in the quantity they can afford.

Merits of Mixed Economy:

  • Merits of capitalist economy and socialist economy are found in mixed economy.
  • There is right of private property and economic freedom. This results in incentive to work hard and capital formation.
  • Price mechanism and competition induces the private sector in efficient decision making and better resource allocation.
  • There is freedom of occupation and consumption.
  • Encourages enterprise and risk taking.
  • Leads to development of technologies through research and development.
  • Economic and social equality is more.

However, mixed economy suffers from uncertainties, excess control by state, poor implementation of plans, high taxes, corruption, wastage of resources, slow growth, lack of efficiency, etc. There are possibilities of private sector growing, disproportionately if state does not maintain a proper balance between public and private sectors.