## Chapter 13 Surface Areas and Volumes Ex 13.8

**Question 1.**
**Find the volume of a sphere whose radius is**
**(i) 7 cm**
**(ii) 0.63 cm**
**Solution:**

(i) We have, r = 7 cm

**Question 2.**
**Find the amount of water displaced by a solid spherical ball of diameter**
**(i) 28 cm**
**(ii) 0.21 m**
**Solution:**

(i) We have, d = 28 cm

⇒ r = 14 cm

**Question 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:**

We have, d = 4.2 cm ⇒ r = 2.1 cm

The density of the metal per cm

^{3}= 8.9 g

The density of the metal 38.808 cm

^{3}= 38.808 x 8.9 g = 345.39 g

Hence, the mass of the ball = 345.39 g

**Question 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:**

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

Diameter = 10.5 cm

⇒ Radius, r = 5.25 cm

**Question 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:**

Inner radius (r_{1}) = 1 m -100 cm

Outer radius (r_{2}) = (100 + 1)cm ( ∵ Inner radius + Thickness)

= 101 cm

**Question 7.**

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

We have, surface area of a sphere = 154 cm^{2}

**Question 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:**

Cost of white washed = ₹ 498.96

Cost of white washing per square metre = ₹ 2.00

**Question 9.**
**Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the**
**(i) radius r’ of the new sphere,**
**(ii) ratio of S and S’.**
**Solution:**

**Question 10.**

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm^{3}) is needed to fill this capsule?
**Solution:**

We have, diameter = 3.5 mm