Volume of Spherical Segment

Theorem

Let $S$ be a spherical segment.

The volume of $S$ is given by the formula:

$V = \dfrac {\pi h \paren {3 {r_1}^2 + 3 {r_2}^2 + h^2} } 6$

where:

$r_1$ and $r_2$ are the radii of the bases of $S$

$h$ is the height of the zone formed by the bases of $S$.

Proof

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Sources

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