Frustum

A frustum is the portion of a solid – normally a cone or pyramid – which lies between two parallel planes cutting the solid. Degenerate cases are obtained for finite solids by cutting with a single plane only.

Pyramidal frusta are a subclass of the prismatoids.

The formula for the volume of the frustum is


 * $$V =\frac{1}{3} h(B1+\sqrt{B1\times B2}+B2)$$

where h is the height from the top base to the bottom base, B1 is the area of the bottom base, and B2 is the area of the top base. A more intuitive formula is: the volume of the cone (or other figure) before you chopped the top off, minus the volume of the cone (or other figure) that you chopped off.

An example of a pyramidal frustum may be seen on the reverse of the Great Seal of the United States, as on the back of the U.S. one-dollar bill. The "unfinished pyramid" is surmounted by the "eye of providence".

Certain ancient Native American mounds also form the frustum of a pyramid.

The focal field of a still or video camera forms a frustum. In 3D computer graphics, this is called the viewing frustum.

The spelling frustrum, listed as "erroneous" by the Oxford English Dictionary, is frequently encountered and might be considered a variant. The OED gives both frusta and frustums for the plural.