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.