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 =
Use π = 3.14
4 × π × a × b × c
3
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
Recent Articles
-
Calculate the Conditional Probability using a Contingency Table
Mar 29, 23 10:19 AM
Learn to calculate the conditional probability using a contingency table. This contingency table can help you understand quickly and painlessly. -
Rational Numbers - Definition and Examples
Mar 15, 23 07:45 AM
To learn about rational numbers, write their decimal expansion, and recognize rational numbers that are repeating decimals and terminating decimals.
100 Tough Algebra Word Problems.
If you can solve these problems with no help, you must be a genius!
