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Volume of an Ellipsoid Formula

Ellipsoid is a geometrical surface, whose all plane sections are either ellipses or circles.Ellipsoid Volume formula is used to find the volume of an ellipsoid. The unit of volume is cubic.

An ellipsoid is a closed quadric surface that is a three-dimensional analogue of an ellipse. The equation reduces to that of the volume of a sphere when all three elliptic radii are equal, and to that of an oblate or prolate spheroid when two of them are equal. The volume of an ellipsoid is two thirds the volume of a circumscribed elliptic cylinder. The volume of an ellipse of dimension higher than 3 can be calculated using the dimensional constant given for the volume of a hypersphere. One can also define ellipsoids in higher dimensions, as the images of spheres under invertible linear transformations. The spectral theorem can again be used to obtain a standard equation akin to the one given above.
 

Related Calculators
Ellipsoid Volume Calculator Cylinder Volume Formula Calculator
Calculate Volume Volume a Sphere
 

Volume Formula of an Ellipsoid

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The volume formula of an ellipsoid is given below,

Examples Volume Formula of an Ellipsoid

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Find below the solved examples of Ellipsoid,

Solved Examples

Question 1:
Find the volume of the ellipsoid whose width, length and height axis radius are 8 cm, 6 cm and 4 cm respectively ?

Solution:
Given,
r1 = 8 cm
r2 = 6 cm
r3 = 4 cm

Volume of the ellipsoid
V = $\frac{4\times \pi\times r_{1}\times r_{2}\times r_{3}}{3}$

V = $\frac{4\times\pi\times8\times6\times4}{3}$

V = $256\pi$

V = 804.247 cm3


Question 2:
Find the volume of the ellipsoid whose width, length and height axis radius are 10 cm, 8 cm and 6 cm respectively ?

Solution:
Given,
r1 = 10 cm
r2 = 8 cm
r3 = 6 cm

Volume of the ellipsoid
V = $\frac{4\times \pi\times r{1}\times r_{2}\times r_{3}}{3}$

V = $\frac{4\times\pi\times10\times8\times6}{3}$

V = $640\pi$

V = 2010.619 cm3


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