Answer
$\frac{dh}{dt} = \frac{8}{9\pi} \approx 0.283 cm/s$
Work Step by Step
Volume of a cone:
$V = \frac{1}{3} \pi r^{2}h$
From proportions:
$\frac{r}{h} = \frac{3}{10}$
Solve for $r$:
$r = \frac{3}{10}h$
$V = \frac{1}{3} \pi (\frac{3}{10}h)^{2}h$
$V = \frac{3}{100} \pi h^{3}$
$\frac{dV}{dt} = \frac{3}{100} \pi 3h^{2} \times \frac{dh}{dt}$
$\frac{dV}{dt} = \frac{3}{100} \pi 3(5)^{2} \times \frac{dh}{dt}$
$\frac{dV}{dt} = \frac{9}{4} \pi \times \frac{dh}{dt}$
Given: $\frac{dV}{dt} = 2$
$2 = \frac{9}{4} \pi \times \frac{dh}{dt}$
Solve for $\frac{dh}{dt}$:
$\frac{dh}{dt} = \frac{2}{\frac{9\pi}{4}}$
$\frac{dh}{dt} = \frac{8}{9\pi} \approx 0.283 cm/s$
