The volume of the truncated pyramid

To find the volume of a truncated pyramid, it is enough to remember one simple formula that includes three unknown parameters. But first, let’s remember what each word of the designated concept describes.


Calculate the volume of a truncated pyramid

The area of the upper base S1
The area of the upper base S2
Height h

Definitions and formulas

Volume (from lat. volume–”filling”) is a quantitative characteristic of the space occupied by a body or substance.

Pyramid (Ancient Greek. the word meaning “memorial cake of a conical shape”) is a polyhedron (polyhedron), in which one face is an [arbitrary] polygon (it is also its base), and all the others (they are considered lateral) are triangles with a common vertex.

Truncation also means a certain “cut-off”.

In other words, it is a part of the pyramid that is enclosed between the base and the plane parallel to it.


Усеченная пирамида

The formula for calculating the volume of a truncated pyramid is as follows:

where h is the height of the “cut” pyramid,

S1 and S2– the areas of its upper and lower bases, respectively.