# Circumference of a circle and perimeter of a semicircle

## Home learning focus

Learn about the circumference of a circle and the perimeter of a semicircle and how to calculate them.

This lesson includes:

- one video
- learning summary
- two activity sheets

# Learn

Students looking to achieve grade 4 in GCSE Maths must understand that the circumference of a circle is always the same distance from the centre. Students must be able to calculate the circumference of a circle and find the perimeter of semicircles.

Read page 2 of our 'Circles, sectors and arcs' Bitesize revision guide to understand:

- what pi is
- how to calculate the circumference of a circle

## What is pi?

For any circle:

circumference ÷ diameter = 3.1415...

This number is **pi** or **π**.

π = 3.14

This means this equations can also be written as:

circumference ÷ diameter = π

The pi symbol (**π**) allows you to give the exact value to a calculation involving circles as pi cannot be written as an exact fraction or decimal. If a decimal answer is required, the value can be approximated as 3.14 (3 significant figures).

Scientific calculators have a **π** button which can be used during calculations, with the final answer being rounded off as appropriate.

## Circumference of a circle

The **circumference** of a circle is the distance around the circle. It is another name for the **perimeter** of a circle.

The circumference of a circle is calculated using the formula:

circumference = π × diameter

This can also be written as:

C = πd

A straight line which joins two points on the circle and passes through the centre is a **diameter**. The distance from the centre of a circle to its circumference is called the **radius**.

The diameter is twice the length of the radius. So, an alternative formula for the circumference of a circle is:

C = π2r

**Worked example**

A circle has a diameter of 10 cm. Work out its circumference, using π = 3.14.

Using the equation C = πd or

circumference = π × diameter this can be solved:

C = 3.14 × 10 = 31.4 cm

C = 31.4 cm

So the circumference of this circle is **31.4 cm**.

Another solution to this problem is to use the equation: C = 2πr

C = 2 × 3.14 (π) × 5 cm (radius)

C = 31.4 cm

## Perimeter of a semicircle

Remember that the perimeter of a shape is the distance **round the outside**.

The perimeter of a semicircle is **half** of the circumference **plus the diameter**.

**Worked example**

Circumference of circle = πd = π × 8 = 25.12 cm

Half of circumference = 12.56 cm

Perimeter = 12.56 + 8 = 20.56 cm

The perimeter of the semicircle is **20.56 cm**.

To learn more about circumference look at the Circles, sectors and arcs Bitesize guide here.

# Practise

## Activity 1

**Circumference**

Complete the activity sheet from Beyond on circumference of a circle to test your knowledge. You can print it out or write your answer on a piece of paper.

Click here to see the correct answers.

## Activity 2

**Perimeter of a semicircle**

Complete the activity sheet from White Rose Maths on perimeter of a semicircle to test your knowledge. You can print it out or write your answer on a piece of paper.

Click here to see the correct answers.

# Choose your exam specification

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# There's more to learn

Have a look at these other resources around the BBC and the web.