Practice Volume of a Sphere in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The amount of three-dimensional space inside a sphere, given by \frac{4}{3}\pi r^3.

Imagine filling a sphere with water, then pouring all that water into a cylinder that has the same radius and a height equal to the sphere's diameter (2r). The sphere fills exactly two-thirds of the cylinder. Archimedes was so proud of discovering this relationship that he had it carved on his tombstone.

Example 1

easy
A basketball has a radius of 12 cm. Find its volume. Leave your answer in terms of \pi.

Example 2

medium
A sphere has a volume of \frac{500\pi}{3} cmยณ. Find its radius.

Example 3

easy
A sphere has a diameter of 10 cm. Find its volume. Leave your answer in terms of \pi.

Example 4

hard
If the radius of a sphere is doubled, by what factor does its volume increase? Prove your answer algebraically.