Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The volume $V$ of a right circular cylinder of height 2 and radius $r$ is $V ( r ) = 2 \pi r ^ { 2 }$. Find the instantaneous rate of change of volume with respect to radius $r$ when $r = 7$.
A) $23 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$
B) $28 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$
C) $98 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$
D) $32 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$

Question

Quizplus · Accepted Answer

The instantaneous rate of change of volume with respect to radius $r$ is found by differentiating $V(r) = 2\pi r^2$ with respect to $r$, giving $dV/dr = 4\pi r$. Substituting $r = 7$ gives $4\pi \times 7 = 28\pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$.

Choose the One Alternative That Best Completes the Statement or Answers