Area of Zone of Sphere

Theorem

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

The area $\AA$ of $\ZZ$ is given by:

$\AA = 2 \pi R h$

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 $h$: $4.41$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): zone
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): zone
  • 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 $h$: $7.41.$
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