Practice Volume of a Cone 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 cone, which is exactly one-third the volume of a cylinder with the same base and height.

Imagine filling a cone-shaped paper cup with water and pouring it into a cylinder of the same width and height. You'd need to fill the cone exactly three times to fill the cylinder. A cone is a cylinder that 'tapers to a point,' losing two-thirds of its volume in the process.

Example 1

easy
A cone has a radius of 6 cm and a height of 9 cm. Find its volume. Leave your answer in terms of \pi.

Example 2

medium
An ice cream cone has a volume of 75\pi cm³ and a radius of 5 cm. Find the height of the cone.

Example 3

easy
A cone and a cylinder have the same radius and height. The cylinder's volume is 90\pi cm³. What is the cone's volume?

Example 4

hard
A cone has a slant height of 13 cm and a radius of 5 cm. Find its volume. (Hint: use the Pythagorean theorem to find the height first.)
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