Calculate the Volume of a Sphere

To calculate the volume of a sphere, you need to know its radius—the distance from its center to its surface. Then, you simply plug that number into the following formula:

Let's try a problem. Because a simple problem where you're given a sphere's radius is too easy, the following sphere problem involves a cube (just to make things interesting!): What's the volume of a basketball in a box (technically, a cube) if the box has a surface area of 486 square inches?

A cube (or any other ordinary box shape) is a special case of a prism, but you don't need to use the fancy-schmancy prism formula, because the surface area of a cube is simply made up of six congruent squares. Call the length of an edge of the cube s. The area of each side is therefore s². The cube has six faces, so its surface area is 6s². Set this equal to the given surface area of 486 square inches and solve for s:

Thus, the edges of the cube are 9 inches, and because the basketball has the same width as the box it comes in, the diameter of the ball is also 9 inches; its radius is half of that, or 4.5 inches. Now you can finish by plugging 4.5 into the volume formula for a sphere:

(By the way, this is slightly more than half the volume of the box, which is 9³, or 729 cubic inches.)