Water flows into a cylindrical tank of radius 7 cm, raising the level at 2 cm/s. How fast is the volume of water increasing?

Explanation

1. 01

   $V = \pi r^{2}h$ with $r = 7$ fixed, so $\frac{dV}{dt} = \pi r^{2}\frac{dh}{dt}$.

2. 02

   $\pi \times 49 \times 2 = 98\pi$ cm³/s.