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Volume of an Ellipsoid Formula

An ellipsoid is a closed quadric surface that is a three-dimensional analogue of an ellipse. The standard equation of an ellipsoid centered at the origin of a Cartesian coordinate system. The spectral theorem can again be used to obtain a standard equation akin to the one given above.

Ellipsoid Formula

The formula of Ellipsoid is given below:

\[\large V=\frac{4}{3}\pi\,a\,b\,c\]

or the formula can also be written as:

\[\large V=\frac{4}{3}\pi\,r1\,r2\,r3\]

Where,
r1= radius of the ellipsoid 1
r2= radius of the ellipsoid 2
r3= radius of the ellipsoid 3

Volume of an Ellipsoid Formula solved examples

Example: The ellipsoid whose radii are given as a = 9 cm, b = 6 cm and v = 3 cm.

Find the volume of ellipsoid.

Solution:

Given,
Radius (a) = 9 cm
Radius (b) = 6 cm
Radius (c) = 3 cm

Using the formula: $V=\frac{4}{3}\pi\,a\,b\,c$

$V=\frac{4}{3}\times\pi\times9\times6\times3$

$V=678.24\,cm^{3}$

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