A cylindrical rod of iron, whose height is equal to the radius of its base, is melted and cast into spherical balls, each of whose radius is half the radius of the base of the rod. Find the number of spherical balls thus made.

6

We know that,

Volume of a sphere = \(\frac{4}{3}\)πR³ 

Volume of a cylinder = πR²H

Let the radius of the rod = 2x

and the height of the rod = 2x

So, the radius of each spherical ball = \(\frac{2x}{2}\) = x

let the number of the balls = a

According to the concept,

π × (2R)² × 2R = \(\frac{4}{3}\) × π × R³ × a

= 8πR³ = \(\frac{4π }{3}\) × R³ × a 

= a = 6