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How to Find the Volume of a Cone (Mathematics Lesson)

How to Find the Volume of a Cone

The volume of a cone is found using the formula:



In this formula, r is the radius of the circle at the base of the cone and h is the height of the cone. The image below shows what we mean by the radius and height:

A Real Example of How to Find the Volume of a Cone

An Example Question

What is the volume of a cone with a circular base with a radius of 5 cm and a height of 10 cm, as shown below?

Step 1
Start with the formula:
Volume = πr2h/3
Don't forget: π is pi (≈ 3.14) and r2 = r × r (r squared) and / means ÷

Step 2
Substitute the radius and the height into the formula. In our example, r = 5 and h = 10.
Volume = π × 52 × 10/3
Volume = π × 5 × 5 × 10 ÷ 3
Volume = π × 250 ÷ 3
Volume = 3.14 × 250 ÷ 3
Volume = 262 cm3
The volume of the cone with a circular base with a radius of 5 cm and a height of 10 cm is 262 cm3.

Another Real Example of How to Find the Volume of a Cone

The slider below shows another real example of how to find the volume of a cone:
Curriculum
Geometry Lessons
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Here is an interactive widget to help you learn about finding the volume of a cone.
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Here's a second test on finding the volume of a cone.
Here's a third test on finding the volume of a cone.
Note

What Is a Cone?

A cone is an object which starts with a circle, and then tapers to a point.

A Cone in a Cylinder


If a cone is placed in a cylinder, the volume of the cone is exactly a third of the volume of the cylinder.

Can you work out why?