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Chapter 13: Surface Areas and Volumes

TEXTBOOK’S EXERCISE – 13.8

1. Find the volume of a sphere whose radius is

(i) 7 cm (ii) 0.63 m

Sol. (i) Here, r = 7 cm

Volume of the sphere = 4/3 πr3

= 4/3 × 22/7 × 7 × 7 × 7 cm3 = 1437 1/3 cm3

(ii) Here, r = 0.63 m

Volume of the sphere = 43 πr3

= 4/3 × 22/7 × (0.63)3 m3 = 1.05 m3 (approx)

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

(i) 28 cm (ii) 0.21 m

Sol. (i) Here, r = 28/2 cm = 14 cm

Volume of water displaced by the spherical ball = 4/3 πr3

= 4/3 × 22/7 × 14 × 14 × 14 cm3

(ii) Here, r = 0 .21/2 m = 0.105 m

Volume of the water displaced by the spherical ball = 4/3 πr3

= 4/3 × 22/7 × 0.105 × 0.105 × 0.105 m3

= 0.004851 m3

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 cm3?

Sol. Here, r = 4.2/2 cm = 2.1 cm

The volume of the ball = 4/3 πr3

= 4/3 × 22/7 × 2.1 × 2.1 × 2.1 cm3 = 38.808 cm3

Density of the metal = 8.9 g/cm3

∴ Mass of the ball = 8.9 × 38.808 g

= 345.39 g (approx)

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?

Sol. Let the diameter of the earth be 2r. Then the radius of the earth = r

So, the diameter of the moon

⇒ The radius of the moon = r/4

The volume of the earth = 4/3 πr3 … (i)

⇒  The volume of the moon

= 1 64 × volume of the earth

Hence, the volume of the moon is 1 64 of the volume of the earth.

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

Sol. Here, r = 10.5/2 cm = 5.25 cm

Volume of the hemispherical bowl = 23 πr3

= 2/3 × 22 7 × 5.25 × 5.25 × 5.25 cm3

= 303 cm3 (approx)

Hence, the hemispherical bowl can hold 303 1000 litres = 0.303 liters of milk.

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