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:

The formula can also be written as V = 

4 × π × a × b × c3Use 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

V_ellipsoid= 

4 × 3.14 × 2 × 4 × 33

V_ellipsoid = 

4 × 3.14 × 2 × 123

V_ellipsoid = 

4 × 3.14 × 243

V_ellipsoid = 

4 × 75.363

V_ellipsoid = 

301.443

V_ellipsoid = 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.

V_ellipsoid = 

4 × π × 4 × 3 × 13

V_ellipsoid = 

4 × π × 4 × 33

V_ellipsoid = 

4 × π × 123

V_ellipsoid = 

48 × π3

V_ellipsoid = 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.

V_ellipsoid = 

4 × π × 0.5 × 2 × 1.53

V_ellipsoid = 

4 × π × 0.5 × 33

V_ellipsoid = 

4 × π × 1.53

V_ellipsoid = 

6 × π3

V_ellipsoid = 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 × 53

150 = 

4 × 3.14 × a × 103

V_ellipsoid = 

4 × 31.4 × a3

150 = 

125.6 × a3

If 2 = 

189

   then, 2 × 9 = 18

By the same fashion, if 150 = 

125.6 × a3

   then, 150 × 3 = 125.6 × a

450 = 125.6 × a

a = 

450125.6
a = 3.5828 cm