# Solids for Which Volume = Mean of Base Areas times Altitude

## Frustum of a Regular Pyramid

Frustum of a regular pyramid is a portion of right regular pyramid included between the base and a section parallel to the base.

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## Frustums

*Frustum* of a pyramid (or cone) is a portion of pyramid (or cone) included between the base and the section parallel to the base not passing through the vertex.

$V = \frac{1}{3}\left( A_1 + A_2 + \sqrt{A_1A_2} \right)h$

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## Derivation of formula for volume of a frustum of pyramid/cone

**Frustum of a pyramid and frustum of a cone**

The formula for frustum of a pyramid or frustum of a cone is given by

$V = \dfrac{h}{3} \left[ \, A_1 + A_2 + \sqrt{A_1A_2} \, \right]$

Where:

h = perpendicular distance between A_{1} and A_{2} (h is called the altitude of the frustum)

A_{1} = area of the lower base

A_{2} = area of the upper base

Note that A_{1} and A_{2} are parallel to each other.

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