Find the volume of the solid generated by revolving the region about the y-axis.
-The region enclosed by the triangle with vertices ( 1, 0), ( 1, 2), ( 3, 2)
A) 26/3 $\pi$
B) 20/3 $\pi$
C) 10/3 $\pi$
D) 4/3 $\pi$

Question

Quizplus · Accepted Answer

The region is a right triangle with base along the y-axis from y=0 to y=2 and a hypotenuse from (1,2) to (3,2). When revolved around the y-axis, it forms a conical frustum. Using the disk method, the volume is calculated as $\pi \int_{0}^{2} (3-y)^2 - (1-y)^2 \, dy$, which evaluates to 20/3 $\pi$.

Find the Volume of the Solid Generated by Revolving the Region