# 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

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

and V = 150 cm3 Vellipsoid =
48 × π / 3

Vellipsoid = 16 π cm3

Example #3

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 1. ### How to Derive the Equation of an Ellipse Centered at the Origin

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.

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons. Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

## Recent Articles 1. ### How to Derive the Equation of an Ellipse Centered at the Origin

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. 