Lateral Surface Area of Frustum of Right Circular Cone

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Theorem

Let $F$ be a frustum of a right circular cone.

The area $\AA$ of the lateral surface of $F$ is given as:

\(\ds \AA\) \(=\) \(\ds \pi \paren {r_1 + r_2} \sqrt {h^2 + \paren {r_2 - r_1}^2}\)
\(\ds \) \(=\) \(\ds \pi \paren {r_1 + r_2} s\)

where:

$r_1$ and $r_2$ are the radii of the bases of $F$
$h$ is the altitude of $F$.
$s$ is the slant height of $F$.


Frustum-of-Cone.png

Proof


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Sources

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