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

AP Calculus ABeasymcq1 pt

The area $A$ of a circle (in cm $^2$ ) is a function of its radius $r$ (in cm), and $A'(5)=10\pi$ . Which statement best interprets $A'(5)=10\pi$ ?

A.The circle's area is

10\pi

cm

^2

.

B.When the radius is 5 cm, the area increases at a rate of

10\pi

cm

^2

per cm of radius.

C.The radius increases at

10\pi

cm per second.

D.The circle's circumference is

10\pi

cm.

Explanation

Core Concept

Since $A'(r)=2\pi r$ , at $r=5$ the derivative is $2\pi(5)=10\pi$ . This is the rate of change of area with respect to radius.

Correct Answer

BWhen the radius is 5 cm, the area increases at a rate of $10\pi$ cm $^2$ per cm of radius.

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