How fast is the water level rising at the moment the tank holds 18π m³ of water?

Explanation

1. 01

   First the depth: $\frac{\pi h^{3}}{12} = 18\pi$ gives $h^{3} = 216$, so $h = 6$.

2. 02

   $2 = \frac{\pi \times 36}{4}\frac{dh}{dt} = 9\pi\frac{dh}{dt}$, so $\frac{dh}{dt} = \frac{2}{9\pi}$ m/min.