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

AP Calculus ABmediummcq1 pt

The circumference of a circle increases at 4 cm/s. How fast is the radius increasing?

A.

\dfrac{1}{\pi}

cm/s

B.

\dfrac{4}{\pi}

cm/s

C.

\dfrac{2}{\pi}

cm/s

D.

4

cm/s

Explanation

Core Concept

Since $C=2\pi r$ , $\dfrac{dC}{dt}=2\pi\dfrac{dr}{dt}$ . Solving $4=2\pi\dfrac{dr}{dt}$ gives $\dfrac{dr}{dt}=\dfrac{2}{\pi}$ cm/s.

Correct Answer

C $\dfrac{2}{\pi}$ cm/s

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