Volume of an ellipsoid 

When the three radii are known, the volume of an ellipsoid can be calculated by using the formula you see below:

Volume of an ellipsoid

The formula can also be written as V =
4 × π × a × b × c / 3
Use π = 3.14

Some examples showing how to find the volume of an ellipsoid.


Example #1


Find V if a = 2 inches, b = 4 inches, and c = 3 inches

Vellipsoid=
4 × 3.14 × 2 × 4 × 3 / 3


Vellipsoid =
4 × 3.14 × 2 × 12 / 3


Vellipsoid =
4 × 3.14 × 24 / 3


Vellipsoid =
4 × 75.36 / 3


Vellipsoid =
301.44 / 3


Vellipsoid = 100.48 inches3


Example #2

Find V if a = 4 cm, b = 3 cm, and c = 1 cm. Express the answer in terms of π.

Vellipsoid =
4 × π × 4 × 3 × 1 / 3


Vellipsoid =
4 × π × 4 × 3 / 3


Vellipsoid =
4 × π × 12 / 3


Vellipsoid =
48 × π / 3


Vellipsoid = 16 π cm3


Example #3

Find V if a = 0.5 cm, b = 2 cm, and c = 1.5 cm. Express the answer in terms of π.

Vellipsoid =
4 × π × 0.5 × 2 × 1.5 / 3


Vellipsoid =
4 × π × 0.5 × 3 / 3


Vellipsoid =
4 × π × 1.5 / 3


Vellipsoid =
6 × π / 3


Vellipsoid = 2 π cm3


Example #4

If the volume of an ellipsoid is V = 150 cm3, b = 2 and c = 5 cm, find a

Just replace everything you know into the formula

150 =
4 × 3.14 × a × 2 × 5 / 3


150 =
4 × 3.14 × a × 10 / 3


Vellipsoid =
4 × 31.4 × a / 3


150 =
125.6 × a / 3


If 2 =
18 / 9
  then, 2 × 9 = 18


By the same fashion, if 150 =
125.6 × a / 3
  then, 150 × 3 = 125.6 × a


450 = 125.6 × a

a =
450 / 125.6

a = 3.5828 cm

Recent Articles

  1. Types of Triangles

    Dec 03, 22 12:47 PM

    Learn to identify 6 types of triangles based on their sides or angles and 7 more types based on both their sides and angles.

    Read More

  2. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes