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

AP Calculus ABmediummcq1 pt

The region enclosed by the graphs of $x=y^2$ and $x=4$ is revolved about the $y$ -axis. What is the volume of the resulting solid?

A.

64\pi

B.

\frac{64\pi}{5}

C.

\frac{256\pi}{5}

D.

\frac{128\pi}{5}

Explanation

Core Concept

The curves meet at $y=\pm2$ . The volume is $\pi\int_{-2}^2(16-y^4)\,dy=\pi[16y-\frac{y^5}{5}]_{-2}^2=\frac{256\pi}{5}$ .

Correct Answer

C $\frac{256\pi}{5}$

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