**Volume by shells** is a method of finding the volume of a solid of revolution. This method involves splitting the shape into indefinitely small rectangles folded into a cylinder shape. The formula for the volume of any solid of rotation is or , depending on which axis the rotation is around. In the case of volume by rings, the formula is

assuming the rotation is around the -axis.

## Examples

To find the volume of the resulting solid when is rotated around the -axis on the interval , one must first solve the equation for . This gives . The interval must then be changed into an interval of , giving . Now it can be substituted into the formula.