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

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