Find the rate of change of the volume of a cone with respect to the radius of its base.
Question:

Find the rate of change of the volume of a cone with respect to the radius of its base.

Solution:

Let V be the volume of the cone. Then,

$V=\frac{1}{3} \pi r^{2} h$

$\Rightarrow \frac{d V}{d r}=\frac{2}{3} \pi r h$