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:

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

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.


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

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



Practise This Question

Tribhuvan Das is an ice-cream scientist and it is his job to make different yet delicious varieties of ice-creams. Before being frozen, ice cream mixtures are in the colloidal state. For months, Tribhuvan Das has been experimenting with new flavours but never got satisfactory results. On a Saturday night just before Diwali, he accidentally mixed up two different samples and got a delicious Sundae. Tribhuvan sent the sample to his boss for tasting, but the boss found it a bit saltier for his palate. It is Diwali time so Tribhuvan is away on leave. The boss is impatient and wants to taste the ice-cream but without the extra saltiness. What should he do?