The necessary equation, for calculating such a volume, *V*, is slightly different depending on which axis is serving as the axis of revolution. These equations note that the lateral surface area of a shell equals: 2 pi (π) multiplied by the cylinder's average radius, *p*(*y*), multiplied by the length of the cylinder, *h*(*y*). One can calculate the volume of a representative shell by: 2π * *p*(*y*) * *h*(*y*) * *dy*, where *dy* is the thickness of the shell -- that being some number approaching zero.

- Horizontal Axis of Revolution
**V = 2π ∫**(*p*)*y*(*h*)*y**dy*

- Vertical Axis of Revolution
**V = 2π ∫**(*p*)*x*(*h*)*x**dx*