Selina Textbook Solutions: Mensuration: Cylinder, Cone and Sphere

 Page 1


Cylinder, Cone & Sphere (Surface Area & Volume) 
 
Exercise 20A 
Question 1. 
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : 
(i) the volume 
(ii) the total surface area. 
 
Solution: 
 
 
Question 2. 
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold? 
 
Solution: 
 
 
Page 2


Cylinder, Cone & Sphere (Surface Area & Volume) 
 
Exercise 20A 
Question 1. 
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : 
(i) the volume 
(ii) the total surface area. 
 
Solution: 
 
 
Question 2. 
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold? 
 
Solution: 
 
 
Question 3. 
 
 
Solution: 
 
 
Question 4. 
How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m 
in diameter? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter. 
Page 3


Cylinder, Cone & Sphere (Surface Area & Volume) 
 
Exercise 20A 
Question 1. 
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : 
(i) the volume 
(ii) the total surface area. 
 
Solution: 
 
 
Question 2. 
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold? 
 
Solution: 
 
 
Question 3. 
 
 
Solution: 
 
 
Question 4. 
How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m 
in diameter? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter. 
Solution: 
 
Question 5. 
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow 
cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long? 
 
 
 
 
 
 
Page 4


Cylinder, Cone & Sphere (Surface Area & Volume) 
 
Exercise 20A 
Question 1. 
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : 
(i) the volume 
(ii) the total surface area. 
 
Solution: 
 
 
Question 2. 
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold? 
 
Solution: 
 
 
Question 3. 
 
 
Solution: 
 
 
Question 4. 
How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m 
in diameter? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter. 
Solution: 
 
Question 5. 
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow 
cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long? 
 
 
 
 
 
 
Solution: 
 
Question 6. 
A cylinder has a diameter of 20 cm. The area of curved surface is 100 sq. cm. Find: 
(i) the height of the cylinder correct to one decimal place. 
(ii) the volume of the cylinder correct to one decimal place. 
Page 5


Cylinder, Cone & Sphere (Surface Area & Volume) 
 
Exercise 20A 
Question 1. 
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : 
(i) the volume 
(ii) the total surface area. 
 
Solution: 
 
 
Question 2. 
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold? 
 
Solution: 
 
 
Question 3. 
 
 
Solution: 
 
 
Question 4. 
How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m 
in diameter? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter. 
Solution: 
 
Question 5. 
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow 
cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long? 
 
 
 
 
 
 
Solution: 
 
Question 6. 
A cylinder has a diameter of 20 cm. The area of curved surface is 100 sq. cm. Find: 
(i) the height of the cylinder correct to one decimal place. 
(ii) the volume of the cylinder correct to one decimal place. 
Solution: 
 
Question 7. 
A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find 
the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g. 
 
Solution: 
Inner radius of the pipe = r = = 2.5 cm 
External radius of the pipe = R = Inner radius of the pipe + Thickness of the pipe 
= 2.5 cm + 0.5 cm 
= 3 cm 
 
Length of the pipe = h = 2 m= 200 cm 
Volume of the pipe = External Volume – Internal Volume