Solve the problem.
-The volume $\mathrm { V }$ of a right circular cylinder of height 2 and radius $\mathrm { r }$ is $\mathrm { V } ( \mathrm { r } ) = 2 \pi \mathrm { r } ^ { 2 }$. 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 the volume formula $V(r) = 2\pi r^2$ with respect to $r$, which gives $dV/dr = 4\pi r$. Substituting $r = 7$ into this derivative gives $4\pi \times 7 = 28\pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$.

Solve the Problem V\mathrm { V }V Of a Right Circular Cylinder of Height 2 and Radius

Solve the Problem $\mathrm { V }$ Of a Right Circular Cylinder of Height 2 and Radius