Question

An iron spherical ball of radius 21cm is melted and it is re-casted in hemispheres of radius 7cm. The number of balls formed is ___.

Answer 1

The volume remains constant.

Let's assume $x$ such hemispherical balls are formed.

So $\frac{4}{3}$ $\pi$ $R^3=x\times$ $\frac{2}{3}$ $\pi$ $r^3$

(Where R is the radius of spherical ball and r is the radius of hemispheres)

$\Rightarrow \frac{4}{3}$ $\pi$ ${21}^3=x\times$ $\frac{2}{3}$ $\pi$ $7^3$

$\Rightarrow x=54$