# Finding the Radius from the Circumference(KS3, Year 7)

## The Lesson

The radius of a circle is found from the circumference of a circle using the formula: In this formula, C is the circumference of the circle. The image below shows what we mean by finding the radius from the circumference: ## How to Find the Radius from the Circumference

Finding the radius from the circumference is easy.

## Question

What is the radius of the circle, with circumference 50 cm, below? # 1

Don't forget: / means ÷ and π is pi (≈ 3.14)

# 2

Substitute the circumference into the formula. In our example, C = 50.

The radius of the circle is 8 cm.

## Lesson Slides

The slider below shows another real example of how to find the radius of a circle from the circumference. Open the slider in a new tab

## Why Is Knowing the Radius in Terms of the Circumference Useful?

Most of the properties of a circle - such as its circumference and area - can be expressed in terms of the radius or diameter. Most students remember the cirumference of a circle with a diameter d as: But what if you are told the radius r instead? Multiply it by 2 to find the diameter. If you substitute 2r for d, a formula for the circumference of a circle in terms of the radius can be found: Read more about how to find the circumference of a circle using the radius
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What is the radius? What is a circle? What is the circumference? Find the radius from the circumference of a circle ( interactive widget)