Solve the problem.
-The area $A = \pi r ^ { 2 }$ of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when $r = 4 \mathrm { ft }$ ?
A) $8 \pi \mathrm { ft } ^ { 2 } / \mathrm { ft }$
B) $4 \pi \mathrm { ft } ^ { 2 } / \mathrm { ft }$
C) $8 \mathrm { ft } ^ { 2 } / \mathrm { ft }$
D) $16 \pi \mathrm { ft } ^ { 2 } / \mathrm { ft }$

Question

Quizplus · Accepted Answer

To find the rate at which the area changes with respect to the radius, differentiate the area formula with respect to $r$, which gives $dA/dr = 2\pi r$. Substituting $r = 4$ ft into this derivative gives $2\pi \times 4 = 8\pi$ square feet per foot.

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Solve the Problem $A = \pi r ^ { 2 }$