Volume of Solids of Revolution Examples

Draw the solid obtained by rotating the region bounded by y = x and y = x² around the line y = 2.

This is a funny-looking that looks like

We label the axis of rotation and draw a mirror copy of the region on the other side of the axis of rotation. We want to make sure the distance from the mirror copy to the axis is the same as the distance from the original region to the axis. Finally, we draw the curved lines that make things look 3-D. Since there's a hole in the middle, we need to draw curved lines for the outside and the inside of the solid.