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

AP Calculus ABmediummcq1 pt

The region bounded by the graph of $x=\sqrt{y}$ , the $y$ -axis, and the line $y=4$ is revolved about the $y$ -axis. What is the volume of the resulting solid?

A.

\frac{16\pi}{3}

B.

8\pi

C.

16\pi

D.

\frac{64\pi}{3}

Explanation

Core Concept

Each cross-section is a disc of radius $\sqrt{y}$ , so $V=\pi\int_0^4 y\,dy=\pi[\frac{y^2}{2}]_0^4=8\pi$ .

Correct Answer

B $8\pi$

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