Finding the Volume of a Cone
(KS3, Year 8)

The Lesson

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:

"Find the Volume" Widget

Here is a widget to help you learn the formulas to find the volumes of different shapes.

How to Find the Volume of a Cone

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-by-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 ÷.

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

Answer:

The volume of the cone with a circular base with a radius of 5 cm and a height of 10 cm is 262 cm3.

Lesson Slides

The slider below shows another real example of how to find the volume of a cone. Open the slider in a new tab

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?
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See Also

What is the radius?