# Problem with finding volume using shells

1. Mar 26, 2015

A solid is generated by revolving the region bounded by y=(1/2)x2 and y= 2 about the y-axis.
So what I did is set up my integral V= 2pi (integral sign from 0 to 2) x(1/2)(x)2 dx
When I solve i get 4pi, and then I have to find the radius of the hole which has one fourth of the volume. So the volume of the hole is pi ( the hole is centered around the axis of revolution which is y-axis). Then I set equal integral from 0 to r (the radius of the hole ) is 2pi(1/2)(x3)dx = pi. the answer i get is 41/2, which is not right as i checked

Last edited: Mar 26, 2015
2. Mar 26, 2015

### Staff: Mentor

This appears to be a homework problem or one in a textbook. @asadpasat, please start a new thread in the Homework and Coursework section (Calculus subsection). This forum section is for conceptual calculus questions, not for homework problems.
Thanks...

Last edited: Mar 26, 2015