Solve the problem.
-The funct $$V ( r ) = 4 \pi r ^ { 2 }$$ describes the volume of a right circular cylinder of height 4 feet and radius r feet. Find the instantaneous rate of change of the volume with respect to the radius when r = 11. Leave answer in terms of $\pi$.

A) $8 \pi$ cubic feet per feet
B) $44 \pi$ cubic feet per feet
C) $22 \pi$ cubic feet per feet
D) $88 \pi$ cubic feet per feet

Question

Solve the problem.
-The funct $$V ( r ) = 4 \pi r ^ { 2 }$$ describes the volume of a right circular cylinder of height 4 feet and radius r feet. Find the instantaneous rate of change of the volume with respect to the radius when r = 11. Leave answer in terms of $\pi$.

A) $8 \pi$ cubic feet per feet
B) $44 \pi$ cubic feet per feet
C) $22 \pi$ cubic feet per feet
D) $88 \pi$ cubic feet per feet

Quizplus · Accepted Answer

The given function $V(r) = 4 \pi r^2$ is incorrect for the volume of a cylinder; it represents the surface area of a sphere. However, assuming it is the function to differentiate, the derivative $V'(r) = 8 \pi r$. Evaluating at $r = 11$, we get $V'(11) = 8 \pi \times 11 = 88 \pi$.

Solve the Problem V(r)=4πr2V ( r ) = 4 \pi r ^ { 2 }V(r)=4πr2

Solve the Problem $V ( r ) = 4 \pi r ^ { 2 }$