# 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 = πr

^{2}h/3**Don't forget:**π is pi (≈ 3.14)

**and**r

^{2}= 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 × 5

Volume = π × 5 × 5 × 10 ÷ 3

Volume = π × 250 ÷ 3

Volume = 3.14 × 250 ÷ 3

Volume = 262 cm

The volume of the cone with a circular base with a radius of 5 cm and a height of 10 cm is 262 cm^{2}× 10/3Volume = π × 5 × 5 × 10 ÷ 3

Volume = π × 250 ÷ 3

Volume = 3.14 × 250 ÷ 3

Volume = 262 cm

^{3}^{3}.

# 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

##### Interactive Test

**show**

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?