Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 37

$(a) V'(r) = 4\pi r^2$ $(b) V'(5) = 100 \pi$

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 $V'(5) = 4 \pi (5^2) = 100 \pi$