A cylindrical rod of iron whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. The number of such spherical balls is

A cylindrical rod with base radius ‘$r$ ’units

Height of the cylinder $h=8r$  units

Volume of the cylinder $=\pi r^{2}h=\pi r^2\left(8r\right)=8\pi r^3$

Radius of the spherical ball $=\frac{r}{2}$

Volume of sphere $=\frac{4}{3}\pi {\left(\frac{r}{2}\right)}^3=\frac{1}{6}\pi r^3$

Number of spherical balls $=\frac{Volumeofcylinder}{Volumeofsphere}=\frac{8\pi r^3}{\frac{1}{6}\pi r^3}=48$