## Calculus (3rd Edition)

$432000\pi\, cm^{3}/min$
$\frac{dV}{dt}=\frac{dV}{dr}\times\frac{dr}{dt}=\frac{d}{dr}(\frac{4}{3}\pi r^{3})\times30\,cm/min$ $=4\pi r^{2}\times30\,cm/min$ As $\frac{dr}{dt}=30\,cm/min$ and $r=0$ at $t=0$, the radius at t=2 min is $2\,min\times30\,cm/min=60\,cm$ Then, $\frac{dV}{dt}|_{t=2\,min}=4\pi(60\,cm)^{2}\times30\,cm/min=432000\pi\, cm^{3}/min$