AP Calculus ABmediummcq1 pt

The surface area of a sphere is S=4πr2S=4\pi r^2. If the radius of a sphere increases at 5 cm/s when r=2r=2 cm, how fast is its surface area increasing?

A.80π80\pi cm2^2/s
B.16π16\pi cm2^2/s
C.40π40\pi cm2^2/s
D.20π20\pi cm2^2/s

Explanation

Core Concept

Differentiating gives dSdt=8πrdrdt=8π(2)(5)=80π\dfrac{dS}{dt}=8\pi r\dfrac{dr}{dt}=8\pi(2)(5)=80\pi cm2^2/s.

Correct Answer

A80π80\pi cm2^2/s

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