Answer
$\frac{1000\pi}{3}cm^{3}/s$
Work Step by Step
The volume of a circular cone is
$V=\frac{1}{3}\pi r^{2}h$
$\frac{dV}{dt}=\frac{1}{3}\pi \times\frac{d}{dt}(r^{2}h)$
Applying the product rule, we have
$\frac{d}{dt}(r^{2}h)=2r\times\frac{dr}{dt}\times h+r^{2}\times\frac{dh}{dt}$
Given: $r=10\,cm$, $h=20\,cm$, $\frac{dr}{dt}=2\,cm/s$ and $\frac{dh}{dt}=2\,cm/s$
Substituting the given values, we get
$\frac{d}{dt}(r^{2}h)=1000\,cm^{3}/s$
Then, $\frac{dV}{dt}=\frac{1}{3}\pi\times1000\,cm^{3}/s=\frac{1000\pi}{3}cm^{3}/s$
