- #1

icesalmon

- 270

- 13

## Homework Statement

A solid is generated by revolving the region bounded by y = x

^{2}/2 and y = 2 around the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the volume is removed. Find the diameter of the hole.

## The Attempt at a Solution

I'm going with cylindrical shells this time around. I'm integrating from x = 0 to x = 2. I think my height is 2-x and my radii are all going to be generated by the function x

^{2}/2. After integration, I get the overall volume is to be 4pi/3. If one quarter of that is taken out after drilling this hole, I have the volume of this figure to be pi. I believe it's a right cylindrical shaped whole, so the volume of a cylinder is pir

^{2}h. I need the radius of one of these cross sections so I need some way to relate the volume. Or maybe I don't, this is where I need assistance. Hopefully I'm not over-thinking this. Thanks.