Volume of Frustum of Cone or Pyramid

Theorem

Let $F$ be a frustum of a cone or a pyramid.

The volume $V$ of $F$ is given as:

$V = \dfrac {h \paren {A_1 + A_2 + \sqrt {A_1 A_2} } } 3$

where:

$A_1$ and $A_2$ are the areas of the bases of $F$
$h$ is the altitude of $F$.


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): frustum
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): frustum
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