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:

Ellipsoid
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.

    Read More

New math lessons

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

            Follow me on Pinterest


Math quizzes

 Recommended

Scientific Notation Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz

Types of angles quiz


Tough algebra word problems

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.

    Read More

K-12 math tests


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.