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:
V =
4
/
3
× π × a × b × c
The formulas can also be written as V =
4 × π × a × b × c
/
3
Use pi = 3.14
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
and V = 150 cm
^{3}
V
_{ellipsoid} =
48 × π
/
3
V
_{ellipsoid} = 16 π cm
^{3}
Example #3
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

Mar 13, 19 11:50 AM
Learn how to derive the equation of an ellipse when the center of the ellipse is at the origin.
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.