CBSE Class 8

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2.

• Direct and Indirect Proportions Class 8 Ex 13.1

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2

Question 1.
Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time is taken for a journey and the distance traveled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time is taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
Solution.
(i) The number of workers on jobs and the time to complete the job are in inverse proportion.
(ii) The time is taken for a journey and the distance traveled in a uniform speed are not in inverse proportion.
(iii) Area of cultivated land and the crop harvested are not in inverse proportion.
(iv) The time taken for a fixed journey and the speed of the vehicle are in inverse proportion.
(v) The population of a country and the area of land per person are in inverse proportion.

Question 2.
In a Television game show, the prize money of  1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners.

Solution.

Question 3.
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.


(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in verse proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?
Solution.
Let the angle (in degree) between a pair of consecutive spokes be \({ y }_{ 3 }\), \({ y }_{ 4 }\) and \({ y }_{ 5 }\) respectively. Then,

Question 4.
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
Solution.
Suppose that each would get \({ y }_{ 2 }\) sweets.
Thus, we have the following table.

Question 5.
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
Solution.
Suppose that the food would last for \({ y }_{ 2 }\) days. We have the following table:

Question 6.
A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
Solution.
Suppose that they take \({ y }_{ 2 }\) days to complete the job. We have the following table

Question 7.
A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?

Solution.
Suppose that \({ y }_{ 2 }\) boxes would be filled. We have the following table:

Question 8.
A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
Solution.
Suppose that \({ x }_{ 2 }\) machines would be required. We have the following table:

Question 9.
A car takes 2 hours to reach a destination by traveling at a speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?
Solution.
Let it take \({ y }_{ 2 }\) hours. We have the following table:
sol.

Question 10.
Two persons could fit new windows in a house in 3 days.
(i) One of the persons fell ill before the work started. How long would the job take now?
(ii) How many persons would be needed to fit the windows in one day?
Solution.
(i) Let the job would take \({ y }_{ 2 }\) days. We have the following table:

Clearly, more the number of persons, lesser would be the number of days to do the job. So, the number of persons and number of days vary in inverse proportion.
So, 2 x 3 = 1 x \({ y }_{ 2 }\)
⇒ \({ y }_{ 2 }\) = 6
Thus, the job would now take 6 days.

(ii) Let \({ y }_{ 2 }\) persons be needed. We have the following table:

Clearly, more the number of persons, lesser would be the number of days to do the job. So, the number of persons and number of days vary in inverse proportion.
So, 3 x 2 = 1 x \({ y }_{ 3 }\)
⇒ \({ T }_{ 2 }\) = 6
Thus, 6 persons would be needed.

Question 11.
A school has 8periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?
Solution.
Let each period be \({ y }_{ 2 }\) minutes long.
We have the following table:

We note that more the number of periods, lesser would be the length of each period. Therefore, this is a case of inverse proportion.
So, 8 x 45 = 9 x \({ y }_{ 2 }\)
⇒ \({ y }_{ 2 }=\frac { 8\times 45 }{ 9 } \)
⇒ \({ y }_{ 2 }\) = 40
Hence, each period would be 40 minutes long.

We hope the NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2.

• Exponents and Powers Class 8 Ex 12.1

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2

Question 1.
Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020 000 000 000 000
(iv) 0.00000000837
(v) 31860000000
Solution.

Question 2.
Express the following numbers in usual form:

Solution.

Question 3.
Express the number appearing in the following statements in standard form:
(i) 1 micron is equal to \(\frac { 1 }{ 1000000 } \)m.
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
(iii) Size of a bacteria is 0.0000005 m
(iv) Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm.
Solution.

Question 4.
In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack ?
Solution.
Total thickness of books
= 5 x 20 mm = 100 mm
Total thickness of paper sheets
= 5 x 0.016 mm = 0.080 mm
∴ Total thickness of the stack
= Total thickness of books + Total thickness of paper sheets
= 100 mm + 0.080 mm
= (100 + 0.080) mm
= 100.080 mm
= 1.0008 x \({ 10 }^{ 2 }\) mm.

We hope the NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4.

• Mensuration Class 8 Ex 11.1
• Mensuration Class 8 Ex 11.2
• Mensuration Class 8 Ex 11.3

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4

Question 1.
Given a cylindrical tank, in which situation will you find the surface area and in which situation volume?
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.
Solution.
(a) Volume
(b) Surface area
(c) Volume.

Question 2.
The diameter of cylinder A is 7 cm, and the height is 14 cm. The diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has a greater surface area?

Solution.

Question 3.
Find the height of a cuboid whose base area is 180 \({ cm }^{ 2 }\) and volume is 900 \({ cm }^{ 3 }\).
Solution.
Height of the cuboid
= \(\frac { Volume\quad of\quad the\quad cuboid }{ Base\quad area\quad of\quad the\quad cuboid } \)
= \(\frac { 900 }{ 180 } \)
= 5 cm

Question 4.
A cuboid is of dimensions 60 cm x 54 cm x 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Solution.
A volume of the cuboid

Question 5.
Find the height of the cylinder whose volume is 1.54 \({ m }^{ 3 }\) and diameter of the base is 140 cm.
Solution.

Question 6.
A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.
Solution.

Question 7.
If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?
Solution.
Let the original edge of the cube be a cm.
Then, its new edge = 2a cm

Question 8.
Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of the reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3.

• Mensuration Class 8 Ex 11.1
• Mensuration Class 8 Ex 11.2
• Mensuration Class 8 Ex 11.4

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3

Question 1.
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

Solution.

Question 2.
A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpau¬lin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Solution.

Question 3.
Find the side of a cube whose surface area is 600 \({ cm }^{ 2 }\).
Solution.
Let the side of the cube be a cm.
Then, Total surface area of the cube = 6\({ a }^{ 2 }\)
According to the question,
6\({ a }^{ 2 }\)= 600
⇒ \({ a }^{ 2 }\) = \(\frac { 600 }{ 6 } \)
⇒ \({ a }^{ 2 }\) = 100
⇒ a = \(\sqrt { 100 } \)
⇒ a = 10 cm
Hence, the side of the cube is 10 cm.

Question 4.
Rukhsar painted the outside of the cabinet of measure 1 m x 2 m x 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?

Solution.

Question 5.
Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth, and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 \({ m }^{ 2 }\) of area is painted.
How many cans of paint will she need to paint the room?
Solution.
l = 15 m
b = 10 m
h = 7 m
Surface area to be painted

Hence, she will need 5 cans of paint to paint the room.

Question 6.
Describe how the two figures at the right are alike and how they are different. Which box has a larger lateral surface area?

Solution.
Similarity → Both have the same heights.
Difference → One is a cylinder, the other is a cube;
The cylinder is a solid obtained by revolving a rectangular area about its one side whereas a cube is a solid enclosed by six square faces; a cylinder has two circular faces whereas a cube has six square faces.

Question 7.
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How many sheets of metal is required?

Solution.

Question 8.
The lateral surface area of a hollow cylinder is 4224 \({ cm }^{ 2 }\). It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
Solution.
Lateral surface area of the hollow cylinder = 4224 \({ cm }^{ 2 }\)

Question 9.
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
Solution.
Diameter of the road roller = 84 cm

Question 10.
A company packages its milk powder in the cylindrical container whose base has a diameter of 14 cm and height 20 cm. The company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2.

• Mensuration Class 8 Ex 11.1
• Mensuration Class 8 Ex 11.3
• Mensuration Class 8 Ex 11.4

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2

Question 1.
The shape of the top surface of a table is a trapezium. Find its area, if its parallel sides are 1 m and 1.2 man the d perpendicular distance between them is 0.8 m.
Solution.
Area of the top surface of the table

= \(\frac { 1 }{ 2 } h(a+b)\)
= \(\frac { 1 }{ 2 } \times 0.8\times (1.2+1)\)
= \(0.88{ m }^{ 2 }\)

Question 2.
The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the another parallel side.
Solution.
Area of trapezium
= \(\frac { 1 }{ 2 } h(a+b)\)

⇒ \(34=\frac { 1 }{ 2 } \times 4(10+b)\)
⇒ \(34=2\times (10+b)\)
⇒ \(10+b=\frac { 34 }{ 2 } \)
⇒ 10 + b=17
⇒ b = 17 – 10
⇒ b = 7 cm
Hence, the length of another parallel side is 7 cm.

Question 3.
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC

Solution.
Fence of the trapezium shaped field ABCD = 120 m
⇒ AB + BC + CD + DA = 120
⇒ AB + 48 + 17 + 40 = 120
⇒ AB + 105 = 120
⇒ AB = 120 – 105
⇒ AB = 15 m
∴ Area of the field
= \(\frac { (BC+AD)\times AB }{ 2 } \)
= \(\frac { (48+40)\times 16 }{ 2 } \) = 660 \({ m }^{ 2 }\)

Question 4.
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

Solution.
Area of the field
= \(\frac { 1 }{ 2 } d({ h }_{ 1 }+{ h }_{ 2 })\)
= \(\frac { 24\times (8+13) }{ 2 } \) = \(\frac { 24\times 21 }{ 2 } \)
= 12 x 21 = 252\({ m }^{ 2 }\)

Question 5.
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Solution.
Area of the rhombus

= \(\frac { 1 }{ 2 } \times { d }_{ 1 }\times { d }_{ 2 }\)
= \(\frac { 1 }{ 2 } \times 7.5\times 12\)
= 45 \({ m }^{ 2 }\)

Question 6.
Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
Solution.
Area of the rhombus
= base (b) x altitude (h) = 5
= 5 x 4.8 = 24 \({ cm }^{ 2 }\)

Question 7.
The floor of a building consists of 3,000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per \({ m }^{ 2 }\) is ₹ 4.
Solution.
Area of a tile

Question 8.
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10,500 \({ m }^{ 2 }\) and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Solution.
Let the length of the side along the road be x m. Then, the length of the side along the river is 2x m.
Area of the field = 10,500 square metres

Question 9.
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
Solution.
Area of the octagonal surface

Question 10.
There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways.

Find the area of this park using both ways. Can you suggest some other way of finding its area ?
Solution.

Question 11.
Diagram of the adjacent picture frame has outer dimensions = 24 cm x 28 cm and inner dimensions 16 cm x 20 cm. Find the area of each section of the frame, if the width of each section the same.

Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2, drop a comment below and we will get back to you at the earliest.