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
easyA basketball has a radius of 12 cm. Find its volume. Leave your answer in terms of \pi.
Example 2
mediumA sphere has a volume of \frac{500\pi}{3} cmยณ. Find its radius.
Example 3
easyA sphere has a diameter of 10 cm. Find its volume. Leave your answer in terms of \pi.
Example 4
hardIf the radius of a sphere is doubled, by what factor does its volume increase? Prove your answer algebraically.