How to Find the Radius of a Sphere When Given the Volume

By Chance E. Gartneer

The radius of a sphere hides inside its absolute roundness. A sphere's radius is the length from the sphere's center to any point on its surface. The radius is an identifying trait, and from it other measurements of the sphere can be calculated, including its circumference, surface area and volume. The formula to determine the volume of a sphere is 4/3π multiplied by r, the radius, cubed, where π, or pi, is a nonterminating and nonrepeating mathematical constant commonly rounded off to 3.1416. Since we know the volume, we can plug in the other numbers to solve for the radius, r.

Multiply the volume by 3. For example, suppose the volume of the sphere is 100 cubic units. Multiplying that amount by 3 equals 300.

Divide this figure by 4π. In this example, dividing 300 by 4π gives a quotient of 23.873.

Calculate the cube root of that number. For this example, the cube root of 23.873 equals 2.879. The radius is 2.879 units.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.