How to Use Volume to Find the Height of a Sphere

By Chance E. Gartneer
The diameter connects the two opposite points on the sphere's surface to its center.
Zedcor Wholly Owned/ Images

When a sphere sits on a flat surface, its diameter sits perpendicular to the surface and creates a 90-degree angle. Because the diameter, the longest straight distance within the sphere, ends with a point that is farthest vertically from the surface, the diameter can also be thought of as the sphere's height. The volume of a sphere is stated as 4/3 * pi * radius^3, where pi is a constant roughly equaling 3.142 and the radius, equal to half the diameter, is the distance from the sphere's center to any point on its surface area. By working the volume formula backwards, you can find the height of the sphere's diameter.

Multiply the volume by 3, then divide it by 4. For an example, let the volume be 900 cubic inches. Multiplying 900 by 3 results in 2,700, and dividing 2,700 by 4 equals 675 cubic inches.

Divide the product by pi. In this example, dividing 675 cubic inches by pi results in approximately 214.859 cubic inches.

Find the cubed root of the product of the previous step to obtain the sphere's radius. In this example, the cubed root of 214.859 cubic inches is approximately 5.989 inches.

Multiply the radius by 2 to obtain the sphere's diameter. Concluding this example, multiplying a radius of 5.989 inches by 2 results in a diameter of 11.978 inches.

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.