# NCERT Solutions for Class 9th Mathematics

## Chapter 13. Surface Areas and Volumes

### Exercise 13.8

**EXERCISE 13.8**

**Assume π = , unless stated otherwise.**

**1. Find the volume of a sphere whose radius is**

**(i) 7 cm (ii) 0.63 m**

**Solution:**

**2. Find the amount of water displaced by a solid spherical ball of diameter**

**(i) 28 cm (ii) 0.21 m**

**Solution:**

**3. The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm ^{3} ?**

**Solution:**

**4. The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?**

**Solution:**

Let diameter of earth = x

**5. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?**

**Solution:**

Diameter = 10.5 , radius = 5.25

**6. A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.**

**Solution:**

Radius = 1.01 m , radius = 1 m

**7. Find the volume of a sphere whose surface area is 154 cm ^{2}.**

**Solution:**

Surface area = 154 cm^{2}

^{}

**8. A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of 498.96. If the cost of white-washing is 2.00 per square metre, find the**

**(i) inside surface area of the dome, (ii) volume of the air inside the dome.**

**Solution:**

**9. Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S**

^{2}**. Find the**

**(i) radius r^{2}**

**of the new sphere, (ii) ratio of S and S**

^{2}**.**

**Solution:**

R = r

**10. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?**

**Solution :**

Diameter = 3.5 mm , r = 1.75 mm