ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress

Question 1.
A square field of side 65 m and rectangular field of length 75 m have the same perimeter. Which field has a larger area and by how much?
Solution:

Question 2.
The shape of a top surface of the table is a trapezium. Find the area if its parallel sides are 1.5 m and 2.5 m and the perpendicular distance between them is 0.8 m.
Solution:

Question 3.
The length and breadth of a hall of a school are 26 m and 22 m respectively. If one student requires 1.1 sq. m area, then find the maximum number of students to be seated in this hall.
Solution:

Question 4.
It costs ₹936 to fence a square field at ₹7·80 per metre. Find the cost of levelling the field at ₹2.50 per square metre.
Solution:

Question 5.
Find the area of the shaded portion in the following figures all measurements are given in cm.

Solution:

Question 6.
Area of a trapezium is 160 sq. cm. Lengths of parallel sides are in the ratio 1:3. If smaller of the parallel sides is 10 cm in length, then find the perpendicular distance between them.
Solution:

Question 7.
The area of a trapezium is 729 cm² and the distance between two parallel sides is 18 cm. If one of its parallel sides is 3 cm shorter than the other parallel side, find the lengths of its parallel sides.
Solution:

Question 8.
Find the area of the polygon given in the figure:

Solution:

Question 9.
The diagonals of a rhombus are 16 m and 12 m, find:
(i) it’s area
(ii) length of a side
(iii) perimeter.
Solution:

Question 10.
The area of a parallelogram is 98 cm². If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.
Solution:

Question 11.
Preeti is painting the walls and ceiling of a hall whose dimensions are 18 m × 15 m × 5 m. From each can of paint 120 m² of area is painted. How many cans of paint does she need to paint the hall?
Solution:

Question 12.
A rectangular paper is size 22 cm × 14 cm is rolled to form a cylinder of height 14 cm, find the volume of the cylinder. (Take π = \(\frac{22}{7}\))
Solution:

Question 13.
A closed rectangular wooden box has inner dimensions 90 cm by 80 cm by 70 cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
Solution:

Question 14.
The lateral surface area of a cuboid is 224 cm². Its height is 7 cm and the base is a square. Find
(i) side of the square base
(ii) the volume of the cuboid.
Solution:

Question 15.
The inner dimensions of a closed wooden box are 2 m by 1.2 m by 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m³ of wood costs ₹5400.
Solution:

Question 16.
A car has a petrol tank 40 cm long, 28 cm wide and 25 cm deep. If the ful consumption of the car averages 13.5 km per litre, how far can the car travel with a full tank of petrol?
Solution:

Question 17.
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area it will cover in 5 revolutions?
Solution:

Question 18.
The capacity of an open cylindrical tank is 2079 m³ and the diameter of its base is 21m. Find the cost of plastering its inner surface at ₹40 per square metre.
Solution:

Question 19.
A solid right circular cylinder of height 1.21 m and diameter 28 cm is melted and recast into 7 equal solid cubes. Find the edge of each cube.
Solution:

Question 20.
(i) How many cubic metres of soil must be dug out to make a well 20 m deep and 2 m in diameter?
(ii) If the inner curved surface of the well in part (i) above is to be plastered at the rate of ₹50 per m², find the cost of plastering.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Area of a parallelogram = base × …….
(ii) Area of a trapezium = \(\frac{1}{2}\) × ……….. × distance between parallel sides.
(iii) Area of a rhombus = \(\frac{1}{2}\) × product of ……..
(iv) Area is measured in ……….. units.
(v) Volume of a solid is the measurement of ………… occupied by it.
(vi) Volume is measured in ………… units.
(vii) The volume of a unit cube is ……….
(viii) 1 litre = …………… cm³
(ix) 1 m³ = ………… litres
(x) Volume of a cuboid = ……….. × height.
(xi) Cylinders in which line segment joining the centres of the circular faces is perpendicular to the base are called ……….
(xii) Volume of a cylinder = area of base × ………..
(xiii) Area of four walls = perimeter of floor × …….
(xiv) Lateral surface area of a cube = 4 × (…………)²
(xv) Total surface area of a cylinder of radius r and height h is ………..
Solution:

Question 2.
State which of the following statements are true (T) or false (F):
(i) Perimeter of a rectangle is the sum of lengths of its four sides.
(ii) Area of a quadrilateral can be found by splitting it into two triangles.
(iiii) Perimeter of a circle of radius r = πr².
(iv) Volume of a cube = 6 × (side)²
(v) 1 m³ = 100000 cm³
(vi) Total surface area of a cuboid
= 2 (lb + bh + hl)
(vii) There is no difference between volume and capacity.
(viii)Total surface area of a cylinder = lateral surface area + area of two circular ends.
(ix) Surface area of a cube = 4 × (side)²
(x) Lateral surface area of a cuboid = perimeter of base × height.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 17):
Question 3.
Area of a triangle is 30 cm². If its base is 10 cm, then its height is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Solution:

Question 4.
If the perimeter of a square is 80 cm, then its area is
(a) 800 cm²
(b) 600 cm²
(c) 400 cm²
(d) 200 cm²
Solution:

Question 5.
Area of a parallelogram is 48 cm². If its height is 6 cm then its base is
(a) 8 cm
(b) 4 cm
(c) 16 cm
(d) none of these
Solution:

Question 6.
If d is the diameter of a circle, then its area is
(a) πd²
(b) \(\frac{\pi d^{2}}{2}\)
(c) \(\frac{\pi d^{2}}{4}\)
(d) 2πd²
Solution:

Question 7.
If the area of a trapezium is 64 cm² and the distance between parallel sides is 8 cm, then sum of its parallel sides is
(a) 8 cm
(b) 4 cm
(c) 32 cm
(d) 16 cm
Solution:

Question 8.
Area of a rhombus whose diagonals are 8 cm and 6 cm is
(a) 48 cm²
(b) 24 cm²
(c) 12 cm²
(d) 96 cm²
Solution:

Question 9.
If the lengths of diagonals of a rhombus is doubled, then area of rhombus will be
(a) doubled
(b) tripled
(c) four times
(d) remains same
Solution:

Question 10.
If the length of a diagonal of a quadrilateral is 10 cm and lengths of the perpendiculars on it from opposite vertices are 4 cm and 6 cm, then area of quadrilateral is
(a) 100 cm²
(b) 200 cm²
(c) 50 cm²
(d) none of these
Solution:

Question 11.
Area of a rhombus is 90 cm². If the length of one diagonal is 10 cm then the length of other diagonal is
(a) 18 cm
(b) 9 cm
(c) 36 cm
(d) 4.5 cm
Solution:

Question 12.
If the volume of a cube is 729 cm³, then its surface area is
(a) 486 cm²
(b) 324 cm²
(c) 162 cm²
(d) none of these
Solution:

Question 13.
If the lateral surface area of a cube is 100 cm², then its volume is
(a) 25 cm³
(b) 125 cm³
(c) 625 cm³
(d) none of these
Solution:

Question 14.
If the length of side of a cube is doubled, then the ratio of volumes of new cube and original cube is
(a) 1 : 2
(b) 2 : 1
(c) 4 : 1
(d) 8 : 1
Solution:

Question 15.
If the dimensions of a rectangular room are 10m × 12m × 9m, then the cost of painting its four walls at the rate of ₹8 per m² is
(a) ₹3186
(b) ₹3618
(c) ₹3168
(d) none of these
Solution:

Question 16.
Volume of a cylinder is 1848 cm². If the diameter of its base is 14 cm, then the height of the cylinder is
(a) 12 cm
(b) 6 cm
(c) 3 cm
(d) none of these
Solution:

Question 17.
If the radius of a cylinder is doubled and height is halved, then new volume is
(a) same
(b) 2 times
(c) 4 times
(d) 8 times
Solution:

Value Based Questions
Question 1.
Pulkit painted four walls and roof of a rectangular room of size 10m × 12m × 12m. He got ₹10 per m² for his work. How much money did he earn? He always gives one-fourth of his income to an orphanage. Find how much money he gave to the orphanage? What values are being promoted?
Solution:

Question 2.
In a slogan writing competition in a school, Rama wrote the slogan ‘Truth pays, never betrays’ on a trapezium shaped cardboard. If the lengths of parallel sides of trapezium are 60 cm and 80 cm and the distance between them is 50 cm, find the area of trapezium. What are the advantages of speaking truth?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
The length of a room is 50% more than its breadth. The cost of carpeting the room at the rate of ₹38.50 m² is ₹924 and the cost of papering the walls at ₹3.30 m² is ₹214.50. If the room has one door of dimensions 1 m × 2 m and two windows each of dimensions 1 m × 1.5 m, find the dimensions of the room.
Solution:

Question 2.
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre? Answer correct to the nearest 100 words.
Solution:

Question 3.
A cylindrical jar is 20 cm high with an internal diameter 7 cm. An iron cube of edge 5 cm is immersed in the jar completely in the water which was originally 12 cm high. Find the rise in the level of water.
Solution:

Question 4.
Squares each of side 6 cm are cut off from the four comers of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps. Find the capacity of the box.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4

Question 1.
The surface area of a cube is 384 cm². Find
(i) the length of an edge
(ii) volume of the cube.
Solution:

Question 2.
Find the total surface area of a solid cylinder of radius 5 cm and height 10 cm. Leave your answer in terms of n.
Solution:

Question 3.
An aquarium is in the form of a cuboid whose external measures are 70 cm × 28 cm × 35 cm. The base, side faces and back face are to be covered with coloured paper. Find the area of the paper needed.
Solution:

Question 4.
The internal dimensions of the rectangular hall are 15 m × 12 m × 4 m. There are 4 windows each of dimension 2 m × 1.5 m and 2 doors each of dimension 1.5 m × 2.5 m. Find the cost of whitewashing all four walls of the hall, if the cost of whitewashing is ₹5 per m². What will be the cost of whitewashing if the ceiling of the hall is also whitewashed?
Solution:

Question 5.
A swimming pool is 50 m in length, 30 m in breadth and 2·5 m in depth. Find the cost of cementing its floor and walls at the rate of ₹27 per square metre.
Solution:

Question 6.
The floor of a rectangular hall has a perimeter 236 m. Its height is 4·5 m. Find the cost of painting its four walls (doors and windows be ignored) at the rate of Rs. 8.40 per square metre.
Solution:

Question 7.
A cuboidal fish tank has a length of 30 cm, a breadth of 20 cm and a height of 20 cm. The tank is placed on a horizontal table and it is three-quarters full of water. Find the area of the tank which is in contact with water.
Solution:

Question 8.
The volume of a cuboid is 448 cm³. Its height is 7 cm and the base is a square. Find
(i) a side of the square base
(ii) surface area of the cuboid.
Solution:

Question 9.
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If its total surface area is 1216 cm², find the volume of the solid.
Solution:

Question 10.
A rectangular room is 6 m long, 5 m wide and 3·5 m high. It has 2 doors of size 1·1 m by 2 m and 3 windows of size 1·5 m by 1·4 m. Find the cost of whitewashing the walls and the ceiling of the room at the rate of ₹5·30 per square metre.
Solution:

Question 11.
A cuboidal block of metal has dimensions 36 cm by 32 cm by 0·25 m. It is melted and recast into cubes with an edge of 4 cm.
(i) How many such cubes can be made?
(ii) What is the cost of silver coating the surfaces of the cubes at the rate of ₹0·75 per square centimetre?
Solution:

Question 12.
Three cubes of silver with edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube, find the cost of coating the surface of the new cube with gold at the rate of ₹3·50 per square centimetre?
Solution:

Question 13.
The curved surface area of a hollow cylinder is 4375 cm², it is cut along its height and formed a rectangular sheet of width 35 cm. Find the perimeter of the rectangular sheet.
Solution:

Question 14.
A road roller has a diameter of 0.7 m and its width is 1.2 m. Find the least number of revolutions that the roller must take in order to level a playground of size 120 m × 44 m.
Solution:

Question 15.
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. 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:

Question 16.
The sum of the radius and height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm². Find the height and the volume of the cylinder.
Solution:

Question 17.
The ratio between the curved surface and total surface of a cylinder is 1 : 2. Find the volume of the cylinder, given that its total surface area is 616 cm³.
Solution:

Question 18.
The given figure showed a metal pipe 77 cm long. The inner diameter of the cross-section is 4 cm and the outer one is 4.4 cm.
Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) total surface area.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.3

Question 1.
The volume of a cube is 343 cm³, find the length of an edge of cube.
Solution:

Question 2.
Fill in the following blanks:

Solution:

Question 3.
Find the height of a cuboid whose volume is 312 cm³ and base area is 26 cm².
Solution:

Question 4.
A godown is in the form of a cuboid of measures 55 m × 45 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 1.25 m³?
Solution:

Question 5.
A rectangular pit 1.4 m long, 90 cm broad and 70 cm deep was dug and 1000 bricks of base 21 cm by 10.5 cm were made from the earth dugout. Find the height of each brick.
Solution:

Question 6.
If each edge of a cube is tripled, then find how many times will its volume become?
Solution:

Question 7.
A milk tank is in the form of cylinder whose radius is 1.4 m and height is 8 m. Find the quantity of milk in litres that can be stored in the tank.
Solution:

Question 8.
A closed box is made of 2 cm thick wood with external dimension 84 cm × 75 cm × 64 cm. Find the volume of the wood required to make the box.
Solution:

Question 9.
Two cylindrical jars contain the same amount of milk. If their diameters are in the ratio 3 : 4, find the ratio of their heights.
Solution:

Question 10.
The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original cylinder?
Solution:

Question 11.
A rectangular piece of a tin of size 30 cm × 18 cm is rolled in two ways, once along its length (30 cm) and once along its breadth. Find the ratio of volumes of two cylinders so formed.
Solution:

Question 12.
Water flows through a cylindrical pipe of internal diameter 7 cm at 5 m per sec. Calculate
(i) the volume in litres of water discharged by the pipe in one minute.
(ii) the time in minutes, the pipe would take to fill an empty rectangular tank of size 4 m × 3 m × 2.31 m.
Solution:

Question 13.
Two cylindrical vessels are filled with milk. The radius of one vessel is 15 cm and the height is 40 cm, and the radius of other vessel is 20 cm and the height is 45 cm. Find the radius of another cylindrical vessel of height 30 cm which may just contain the milk which is in the two given vessels.
Solution:

Question 14.
A wooden pole is 7 m high and 20 cm in diameter. Find its weight if the wood weighs 225 kg per m³ .
Solution:

Question 15.
A cylinder of the maximum volume is cut from a wooden cuboid of length 30 cm and cross-section a square of side 14 cm. Find the volume of the cylinder and the volume of the wood wasted.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.2

Question 1.
Each side of a rhombus is 13 cm and one diagonal is 10 cm. Find
(i) the length of its other diagonal
(ii) the area of the rhombus
Solution:

Question 2.
The cross-section ABCD of a swimming pool is a trapezium. Its width AB = 14 m, depth at the shallow end is 1-5 m and at the deep end is 8 m. Find the area of the cross-section.

Solution:

Question 3.
The area of a trapezium is 360 m², the distance between two parallel sides is 20 m and one of the parallel side is 25 m. Find the other parallel side.
Solution:

Question 4.
Find the area of a rhombus whose side is 6.5 cm and altitude is 5 cm. If one of its diagonal is 13 cm long, find the length of other diagonal.
Solution:

Question 5.
From the given diagram, calculate
(i) the area of trapezium ACDE
(ii) the area of parallelogram ABDE
(iii) the area of triangle BCD.

Solution:

Question 6.
The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively. If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.
Solution:

Question 7.
The perimeter of a trapezium is 52 cm. If its non-parallel sides are 10 cm each and its altitude is 8 cm, find the area of the trapezium.
Solution:

Question 8.
The area of a trapezium is 540 cm². If the ratio of parallel sides is 7 : 5 and the distance between them is 18 cm, find the lengths of parallel sides.
Solution:

Question 9.
Calculate the area enclosed by the given shapes. All measurements are in cm.

Solution:

Question 10.
From the adjoining sketch, calculate
(i) the length AD
(ii) the area of trapezium ABCD
(iii) the area of triangle BCD

Solution:

Question 11.
Diagram of the adjacent picture frame has outer dimensions = 28 cm × 32 cm and inner dimensions 20 cm × 24 cm. Find the area of each section of the frame, if the width of each section is same.

Solution:

Question 12.
In the given quadrilateral ABCD, ∠BAD = 90° and ∠BDC = 90°. All measurements are in centimetres. Find the area of the quadrilateral ABCD.

Solution:

Question 13.
Top surface of a raised platform is in the shape of a regular octagon as shown in the given figure. Find the area of the octagonal surface.

Solution:

Question 14.
There is a pentagonal shaped park as shown in the following figure:
For finding its area Jaspreet and Rahul 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 15.
In the diagram, ABCD is a rectangle of size 18 cm by 10 cm. In ∆ BEC, ∠E = 90° and EC = 8 cm. Find the area enclosed by the pentagon ABECD.

Solution:

Question 16.
Polygon ABCDE is divided into parts as shown in the given figure. Find its area if AD = 8 cm, AH = 6 cm, AG = 4 cm, AF = 3 cm and perpendiculars BF = 2 cm, CH = 3 cm, EG = 2.5 cm.

Solution:

Question 17.
Find the area of polygon PQRSTU shown in 1 the given figure, if PS = 11 cm, PY = 9 cm, PX = 8 cm, PW = 5 cm, PV = 3 cm, QV = 5 cm, UW = 4 cm, RX = 6 cm, TY = 2 cm.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths