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

AP Calculus ABeasymcq1 pt

The region bounded by the graph of $y=2x$ , the $x$ -axis, and the line $x=2$ is revolved about the $x$ -axis. What is the volume of the resulting solid?

A.

4\pi

B.

\frac{8\pi}{3}

C.

\frac{32\pi}{3}

D.

32\pi

Explanation

Core Concept

Each cross-section is a disc of radius $2x$ , so $V=\pi\int_0^2(2x)^2\,dx=\pi[\frac{4x^3}{3}]_0^2=\frac{32\pi}{3}$ .

Correct Answer

C $\frac{32\pi}{3}$

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