How fast is the area of the water surface growing when the water is 4 m deep?

Explanation

1. 01

   $A = \pi r^{2} = \frac{\pi h^{2}}{4}$, so $\frac{dA}{dt} = \frac{\pi h}{2}\frac{dh}{dt}$.

2. 02

   At $h = 4$, $\frac{dh}{dt} = \frac{1}{2\pi}$: $\frac{dA}{dt} = 2\pi \times \frac{1}{2\pi} = 1$ m²/min.