## Calculus, 10th Edition (Anton)

$(a) V'(r) = 4\pi r^2$ $(b) V'(5) = 100 \pi$
If $V(r) = \frac{4}{3} \pi r^3$, then $V'(r) = (3)\frac{4}{3} \pi r^{3-1} \iff V'(r) = 4 \pi r^2$ Instantaneous rate of change of $V$ with respect to $r$ when $r=5$ is $V'(5) = 4 \pi (5^2) = 100 \pi$