Volume of Ellipsoid

Theorem

Let $\EE$ be an ellipsoid such that:

the semimajor axis of $\EE$ is $a$
the semimean axis of $\EE$ is $b$
the semiminor axis of $\EE$ is $c$.

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

$\VV = \dfrac {4 \pi a b c} 3$


Proof


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Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Ellipsoid of Semi-axes $a, b, c$: $4.47$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ellipsoid
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ellipsoid
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Ellipsoid of Semi-axes $a, b, c$: $7.47.$
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