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Finding the Volume of a Cone

(KS3, Year 8)

Let's start with a test!

The Test

Here is a -question, multi-choice test for the "Finding the Volume of a Cone" lesson. The pass mark is 90%. Don't worry! All the information you need to pass is in the lesson section under the test.

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The Lesson

The volume of a cone is found using the formula: volume cone 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: cone radius height1

"Find the Volume" Widget

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

Click on the shape you're learning about.
Click on the pad to start.
Follow the instructions in the bottom-left corner.
On the last click, the formula, workings, and answer will appear in the yellow box.
Enjoy!

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? cone radius height

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.

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?

This page was written by Stephen Clarke.