Apentix/AP Calculus AB/Unit 4: Contextual Applications of Differentiation/Question

AP Calculus ABmediummcq1 pt

A spherical balloon's radius grows at 2 cm/s. How fast does its volume grow when the radius is 3 cm?

A.

36\pi

cm

^3

/s

B.

12\pi

cm

^3

/s

C.

9\pi

cm

^3

/s

D.

72\pi

cm

^3

/s

Explanation

Core Concept

Differentiating $V=\dfrac{4}{3}\pi r^3$ gives $\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}=4\pi(9)(2)=72\pi$ cm $^3$ /s.

Correct Answer

D $72\pi$ cm $^3$ /s

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