Find the rate of change of the volume of a ball with respect to its radius r.

Let V be the volume of the spherical ball. Then,

$V=\frac{4}{3} \pi r^{3}$

$\Rightarrow \frac{d V}{d r}=4 \pi r^{2}$'

Thus, the rate of change of the volume of the sphere is $4 \pi r^{2}$.

When $r=2 \mathrm{~cm}$

$\left(\frac{d V}{d r}\right)_{r=2}=4 \pi(2)^{2}$

$=16 \pi \mathrm{cm}^{3} / \mathrm{cm}$