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:
or the formula can also be written as:
a = r1 = Radius of the ellipsoid of axis 1
b = r2 = Radius of the ellipsoid of axis 2
c = r3 = 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.
Radius (a) = 9 cm
Radius (b) = 6 cm
Radius (c) = 3 cm
Using the formula: