JAMB 2001 · UME · Q36

Find the rate of change of the volume $V$ of a sphere with respect to its radius $r$ when $r = 1$ .

Worked solution (try it first)

The volume of a sphere is $V = \frac43\pi r^3$ .
Differentiate: $\frac{dV}{dr} = 3 \times \frac43\pi r^2$
$= 4\pi r^2$ .
At $r = 1$ : $\frac{dV}{dr} = 4\pi$ , option A.

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