A right circular cylinder is obtained by revolving the region enclosed by the line $x = r$, the $x$-axis, and the line $y = h$, about the $y$-axis. Find the volume of the cylinder.
A) $\pi \mathrm { rh }$
B) $2 \pi r ^ { 2 } \mathrm {~h}$
C) $\pi \mathrm { rh } ^ { 2 }$
D) $\pi r ^ { 2 } h$

Question

Quizplus · Accepted Answer

When the region is revolved about the $y$-axis, it generates a cylinder with radius $r$ and height $h$. Therefore, the volume of the cylinder is $\pi r^2 h$, which is option D.

A Right Circular Cylinder Is Obtained by Revolving the Region x=rx = rx=r

A Right Circular Cylinder Is Obtained by Revolving the Region $x = r$