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

AP Calculus ABmediummcq1 pt

The region bounded by the graph of $y=x^2$ , the $x$ -axis, and the line $x=1$ is revolved about the $x$ -axis. What is the volume of the resulting solid?

A.

\frac{\pi}{3}

B.

\frac{\pi}{2}

C.

\frac{\pi}{5}

D.

\frac{\pi}{7}

Explanation

Core Concept

Each cross-section is a disc of radius $x^2$ , so $V=\pi\int_0^1 x^4\,dx=\pi[\frac{x^5}{5}]_0^1=\frac{\pi}{5}$ .

Correct Answer

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

More Unit 8: Applications of Integration practice questions

hardThe base of a solid is the region bounded by the graphs of $x=y^2$ and $x=4$. Cross sections perpendicular to the $y$-axis are squares. What…
hardThe base of a solid is the region in the first quadrant bounded by the graph of $y=x^2$, the $x$-axis, and the line $x=2$. Cross sections pe…
hardThe base of a solid is the region bounded by the graph of $y=x^2$ and the line $y=4$. Cross sections perpendicular to the $y$-axis are squar…
hardThe base of a solid is the region bounded by the graph of $y=1-x^2$ and the $x$-axis. Cross sections perpendicular to the $x$-axis are equil…
mediumThe base of a solid is the region bounded by the graph of $y=1-x^2$ and the $x$-axis. Cross sections perpendicular to the $x$-axis are semic…

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 8: Applications of Integration Questions →