# 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 × 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

V

_{ellipsoid}=

4 × 3.14 × 2 × 4 × 3
/
3

V

_{ellipsoid} =

4 × 3.14 × 2 × 12
/
3

V

_{ellipsoid} =

4 × 3.14 × 24
/
3

V

_{ellipsoid} =

4 × 75.36
/
3

V

_{ellipsoid} =

301.44
/
3

V

_{ellipsoid} = 100.48 inches

^{3}
**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 × 1
/
3

V

_{ellipsoid} =

4 × π × 4 × 3
/
3

V

_{ellipsoid} =

4 × π × 12
/
3

V

_{ellipsoid} =

48 × π
/
3

V

_{ellipsoid} = 16 π cm

^{3}
**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 × 1.5
/
3

V

_{ellipsoid} =

4 × π × 0.5 × 3
/
3

V

_{ellipsoid} =

4 × π × 1.5
/
3

V

_{ellipsoid} =

6 × π
/
3

V

_{ellipsoid} = 2 π cm

^{3}
**Example #4**
If the volume of an ellipsoid is V = 150 cm

^{3}, 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

V

_{ellipsoid} =

4 × 31.4 × 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 = 3.5828 cm