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.

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 theÂ ellipsoid 1

r2= radius of theÂ ellipsoid 2

r3= radius of theÂ 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:Â $V=\frac{4}{3}\pi\,a\,b\,c$

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

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