Answer
$\approx$ $0.38$ $ft/min$
Work Step by Step
we are given than
$\frac{dV}{dt}$ = $30$ $ft^{3}/min$
$V$ = $\frac{1}{3}{\pi}r^{2}h$ = $\frac{1}{3}{\pi}(\frac{h}{2})^{2}h$ = $\frac{{\pi}h^{3}}{12}$
$\frac{dV}{dt}$ = $\frac{dV}{dh}\frac{dh}{dt}$
$30$ = $\frac{{\pi}h^{2}}{4}\frac{dh}{dt}$
$\frac{dh}{dt}$ = $\frac{120}{{\pi}h^{2}}$
$h$ = $10$ $ft$
$\frac{dh}{dt}$ = $\frac{120}{{\pi}10^{2}}$ $\approx$ $0.38$ $ft/min$
