What is the rate of change of the volume of a sphere with respect to its radius when the radius is 3 cm?

Explanation

1. 01

   $\frac{dV}{dr} = \frac{d}{dr}\left(\frac{4}{3}\pi r^{3}\right) = 4\pi r^{2}$.

2. 02

   At $r = 3$: $36\pi$.