JAMB 2004 · UME · Q38

What is the rate of change of the volume $V$ of a hemisphere with respect to its radius $r$ when $r = 2$ ?

Worked solution (try it first)

A hemisphere is half a sphere, so $V = \frac12 \times \frac43\pi r^3$
$= \frac23\pi r^3$ .
Differentiate: $\frac{dV}{dr} = 2\pi r^2$ .
At $r = 2$ : $2\pi \times 4 = 8\pi$ , option C.