Solve the problem.
-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) $\pi \mathrm { rh } ^ { 2 }$
B) $\pi \mathrm { rh }$
C) $2 \pi r ^ { 2 } h$
D) $\pi r ^ { 2 } h$

Question

Quizplus · Accepted Answer

The region enclosed by the line $x=r$, the $x$-axis, and the line $y=h$ is a rectangle with length $h$ and width $r$. 
When this rectangle is revolved about the $y$-axis, it forms a cylinder with radius $r$ and height $h$. 
Therefore, the volume of this cylinder is given by the formula for the volume of a cylinder: 
$$V = \pi r^2h$$ 
which is option D.

Solve the Problem x=rx = rx=r , The xxx -Axis, and the Line

Solve the Problem $x = r$ , The $x$ -Axis, and the Line