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

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