Ratios of volumes of a cone, sphere and cylinder of the same radius and height

The radius of the circular disks, defined such that the x-axis cuts perpendicularly through them, is

where y or z can be taken to represent the radius of a disk at a particular x value.

Using y as the disk radius, the volume of the sphere can be calculated as

The cone is a type of pyramidal shape. The fundamental equation for pyramids, one-third times base times altitude, applies to cones as well.