Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

The region enclosed by the graphs of $y=\sqrt{x}$ and $y=\frac{x}{2}$ is revolved about the $x$ -axis. What is the volume of the resulting solid?

A.

8\pi

B.

\frac{8\pi}{3}

C.

\frac{16\pi}{3}

D.

\frac{40\pi}{3}

Explanation

Core Concept

The curves intersect at $x=0$ and $x=4$ . The volume is $\pi\int_0^4(x-\frac{x^2}{4})\,dx=\pi(8-\frac{16}{3})=\frac{8\pi}{3}$ .

Correct Answer

B $\frac{8\pi}{3}$

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