A solid sphere of radius 3 𝑐𝑚 is melted and then recast into small spherical balls each of diameter 0. 6 𝑐𝑚. Find the number of balls.

We are given that a solid sphere is melted and recast into small spherical balls. Next, we have to find the number of balls formed.
The radius of the solid sphere, 𝑅 = 3 𝑐𝑚
And the diameter of each spherical ball, 𝑑 = 0. 6 𝑐𝑚
So, the radius of each spherical ball, 𝑟 = 𝑑/2
⇒ 𝑟 = 0.6/2 
⇒ 𝑟 = 0. 3 𝑐𝑚
When a solid is converted from one shape to another, the volume of the solid remains unaltered.
This is because the volume of a solid is the amount of three-dimensional space occupied by the solid. Therefore, whatever the shape of the solid, it will occupy the same amount of space. Let 𝑥 be the total number of spherical balls formed.
So, the volume of a solid sphere = 𝑛 × volume of each spherical ball The volume of the solid sphere, 𝑉 = 4/3 π𝑅³
⇒ 𝑉 = 4/3 × (22/7) × 3 × 3 × 3
⇒ 𝑉 = 792/7
⇒ 𝑉 = 113. 14 𝑐𝑚³
The volume of each spherical ball, 𝑣 = 4/3 π𝑟³
⇒ 𝑣 = 4/3 × 22/7 × 0. 3 × 0. 3 × 0. 3
⇒ 𝑣 = 0.792 
⇒ 𝑉 = 0. 113 𝑐𝑚³
So, the number of spherical balls formed, 𝑛 = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑 𝑠𝑝ℎ𝑒𝑟𝑒 /𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑠𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 𝑏𝑎𝑙𝑙
n = 113.14 / 0.11314
⇒ 𝑛 = 1000
Hence, 1000 spherical balls are formed during recasting