Question

An iron spherical ball of radius $21cm$ is melted and re-casted in spheres of radius $7cm.$ The number of spheres formed will be ___

Answer 1

Given-

Radius of iron spherical ball $=R=21cm$

After melt radius of sphere $=r=7cm$

$\because$After melting and re-casting, the volume remains constant.

Let's assume $x$ such spherical balls will be formed.

So $\frac{4}{3}\pi R^3=x\times \frac{2}{3}\pi r^3$
$\frac{4}{3}\times \frac{22}{7}\times (21{)}^3=x\times \frac{2}{3}\times \frac{22}{7}\times (7{)}^3$
$\Rightarrow 2\times {21}^3=x\times 7^3$

$\Rightarrow x=\frac{2\times {21}^3}{7^3}=54$