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

\[\large V=\frac{4}{3}\pi\,r_1\,r_2\,r_3\]

Where,

a = r_{1} = Radius of the ellipsoid of axis 1

b = r_{2} = Radius of the ellipsoid of axis 2

c = r_{3} = Radius of the ellipsoid of axis 3

**Volume of an Ellipsoid Formula Solved Example**

**Example: **The ellipsoid whose radii are given as a = 9 cm, b = 6 cm and c = 3 cm. Find the volume of an ellipsoid.

**Solution:**

Given,

Radius (a) = 9 cm

Radius (b) = 6 cm

Radius (c) = 3 cm

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

$V=\frac{4}{3}\times 3.14\times9\times6\times3$

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