NCERT Solutions for Class 8 Maths Chapter 9 – Mensuration Ex 9.3

NCERT Solutions for Class 8 Maths Chapter 9 – Mensuration Ex 9.3 are given here in simple, step-by-step form. NCERT stands for National Council of Educational Research and Training, the body that makes your textbook. Exercise 9.1 was about area and Exercise 9.2 about surface area. Exercise 9.3 is about volume. Volume is the amount of space a solid takes up, and capacity is how much a container can hold. This exercise covers the cuboid, the cube and the cylinder.

This exercise has 8 questions. They are based on real objects, such as a matchbox, a water tank, a cylindrical drum, and containers that hold milk or water. You will also change between millilitres, litres and cubic centimetres. Every question below is solved in short steps, with the final answer in bold. Students can use this page for homework and revision, parents can use it to check the work at home, and teachers can use it in class. A free printable PDF of these solutions is also available for offline study.

NCERT Solutions for Class 8 Maths Chapter 9 – Mensuration Ex 9.3

Mensuration
Easy
Q.
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 m and perpendicular distance between them is 0.8 m.
 
Mensuration
Easy
Q.
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 other parallel side.
Mensuration
Easy
Q.
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Mensuration
Medium
Q.
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 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Mensuration
Medium
Q.
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?
 
Mensuration
Easy
Q.
Find the side of a cube whose surface area is 600 cm2.
Mensuration
Easy
Q.
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?
Mensuration
Difficult
Q.
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.
 
Mensuration
Easy
Q.
Given a cylindrical tank, in which situation will you find 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.
 
Mensuration
Easy
Q.
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
Mensuration
Difficult
Q.
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Mensuration
Medium
Q.
Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?
Mensuration
Medium
Q.
A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?
Mensuration
Medium
Q.
Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
 

NCERT Solutions for Class 8 Maths Chapter 9 – Mensuration Ex 9.3

Volume Formulas and Units

  • Cuboid: Volume = length × breadth × height = l × b × h.
  • Cube (side a): Volume = a3.
  • Cylinder (radius r, height h): Volume = πr2h.
  • Take π as 22/7 when the radius is a multiple of 7, otherwise use 3.14.
  • Unit changes: 1 litre = 1000 mL, 1 cm3 = 1 mL, so 1 litre = 1000 cm3. Also 1 m3 = 10,00,000 cm3 = 1000 litres.

Exercise 9.3 – Questions and Answers

Q1. Given a cylindrical tank, in which situation will you find 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.

Answer:
(a) We will find the volume, because how much a tank can hold is its capacity, which is the space inside it.
(b) We will find the surface area, because plastering is done on the outer covering of the tank.
(c) We will find the volume, because we need to compare the water the big tank holds with the water a smaller tank holds.

Q2. Diameter of cylinder A is 7 cm, and the height is 14 cm. 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 greater surface area.

Answer:
The heights and diameters of these cylinders A and B are interchanged.
If the measures of 'r' and 'h' are same, then the cylinder with the greater radius will have the greater volume, because in the formula the radius is squared but the height is not.

Radius of cylinder A = 7/2 cm
Radius of cylinder B = 14/2 cm = 7 cm

As the radius of cylinder B is greater, therefore, the volume of cylinder B will be greater.

Let us verify it by calculating the volume of both the cylinders.

Volume of cylinder A = πr²h
= (22/7 × 7/2 × 7/2 × 14) cm³
= 539 cm³

Volume of cylinder B = πr²h
= (22/7 × 7 × 7 × 7) cm³
= 1078 cm³

Hence, the volume of cylinder B is greater.

Now for the surface areas:

Surface area of cylinder A = 2πr(h + r)
= [2 × 22/7 × 7/2 × (7/2 + 14)] cm²
= [22 × (7 + 28)/2] cm²
= [22 × 35/2] cm²
= 385 cm²

Surface area of cylinder B = 2πr(h + r)
= [2 × 22/7 × 7 × (7 + 7)] cm²
= [44 × 14] cm²
= 616 cm²

Thus, the surface area of cylinder B is also greater than the surface area of cylinder A.

Q3. Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³.

Answer:
Base area of the cuboid = 180 cm²
⇒ Length × Breadth = 180 cm²

Volume of cuboid = Length × Breadth × Height
⇒ 900 cm³ = 180 cm² × Height
⇒ Height = 900/180
= 5 cm

Thus, the height of the cuboid is 5 cm.

Q4. A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Answer:
Volume of cuboid = 60 cm × 54 cm × 30 cm = 97200 cm³

Side of the cube = 6 cm
Volume of the cube = (6)³ cm³ = 216 cm³

Required number of cubes = Volume of the cuboid / Volume of the cube
= 97200 cm³ / 216 cm³
= 450

∴ 450 cubes can be placed in the given cuboid.

Q5. Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm.

Answer:
Given,
Volume of cylinder = 1.54 m³
Diameter of the base = 140 cm
⇒ Radius of the base = (140/2) cm = 70 cm = 70/100 m

Volume of cylinder = πr²h
1.54 m³ = 22/7 × 70/100 × 70/100 × h
⇒ h = (1.54 × 100) / (22 × 7) m
= 154/154 m
= 1 m

Thus, the height of the cylinder is 1 m.

Q6. 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 litres that can be stored in the tank.

Answer:
Radius of cylinder = 1.5 m
Length of cylinder = 7 m

Volume of cylinder = πr²h
= 22/7 × 1.5 × 1.5 × 7
= 49.5 m³

We know that, 1 m³ = 1000 L

∴ The quantity of milk in litres = (49.5 × 1000) L
= 49500 L

Therefore, 49500 L of milk can be stored in the tank.

Q7. Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

Answer:
Volume of cuboidal reservoir = 108 m³
= (108 × 1000) L
= 108000 L

It is given that water is being poured at the rate of 60 L per minute.
i.e. (60 × 60) L = 3600 L per hour

Required number of hours = 108000 / 3600
= 30 hours

∴ It will take 30 hours to fill the reservoir.

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