Volume of Zone of One Base

Theorem

Let $\ZZ$ be a zone of one base of a sphere $\SS$.

The volume $\VV$ of $\ZZ$ is given by:

$\VV = \dfrac {\pi h^2 \paren {3 R - h} } 3$

where:

$R$ is the radius of $\SS$
$h$ is the height of $\ZZ$.


Proof


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Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Spherical Cap of Radius $r$ and Height $h$: $4.40$
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Spherical Cap of Radius $r$ and Height $h$: $7.40.$
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