Answer
$\approx$ $289.25$ $cm^{3}/min$
Work Step by Step
If $C$ = the rate at which water is pumped in then
$\frac{dV}{dt}$ = $C-10000$
$V$ = $\frac{1}{3}{\pi}r^{2}h$
$\frac{r}{2}$ = $\frac{h}{6}$
$r$ $\approx$ $\frac{h}{3}$
$V$ = $\frac{1}{3}{\pi}(\frac{h}{3})^{2}h$ = $\frac{\pi}{27}h^{3}$
$\frac{dV}{dt}$ = $\frac{\pi}{9}h^{2}\frac{dh}{dt}$
$h$ = $200$ $cm$, $\frac{dh}{dt}$ = $20$ $cm/min$
$C-10000$ = $\frac{\pi}{9}200^{2}(20)$
$C$ = $289.25$ $cm^{3}/min$
