Question

A large spherical ball of a radius of 9 cm is formed by combining 8 small spherical balls. Find the radius of one small spherical ball.

1. 3 cm
2. 4.5 cm
3. 6 cm
4. 7.5 cm

Answer 1

Correct Answer - Option 2 : 4.5 cm

Given:

Radius of large ball = 9 cm

Number of small balls = 8

Concepts used:

The volume of spherical ball = 4πr³/3

Calculation:

Let the radius of the small ball be r cm.

The volume of small spherical ball = 4π × (r)³/3 cm³

The volume of large spherical ball = 4π × (9)³/3 cm³

⇒ 972π cm³

Number of small spherical balls = Volume of large spherical ball/volume of small spherical ball

⇒ 8 = 972π cm³/{4π × (r)³/3} cm³

⇒ 8 = 729π cm³/π(r)³ cm³

⇒ r = (729/8)^1/3 cm

⇒ r = (9/2)^{3 × 1/3} cm

⇒ r = 4.5 cm                                                          

∴ Radius of small spherical ball is 4.5 cm.