#### Class nine Surface Areas Volumes Maths NCERT Sol

## 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 πr^{3}

= 4/3 × 22/7
× 7 × 7 × 7 cm^{3} = 1437 1/3 cm^{3
}

(ii) Here, r = 0.63 m

Volume of the sphere
= 43 πr^{3}

= 4/3 × 22/7
× (0.63)^{3} m^{3} = 1.05 m^{3} (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 πr^{3}

= 4/3 × 22/7 × 14 × 14 × 14 cm^{3}

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

Volume of the water
displaced by the spherical ball = 4/3 π*r*^{3}

= 4/3 × 22/7
× 0.105 × 0.105 × 0.105 m^{3}

=
0.004851 m^{3}

**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 π*r*3

= 4/3 × 22/7
× 2.1 × 2.1 × 2.1 cm^{3} = 38.808 cm^{3}

Density of the metal
= 8.9 g/cm^{3}

∴ 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 πr^{3} … (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 πr^{3}

= 2/3 × 22 7 × 5.25 × 5.25 × 5.25 cm^{3}

= 303 cm^{3}
(approx)

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