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
Revise -  the circumference of circles

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.

Circumference of a circle

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.

Perimeter of a circle

Click here to see the correct answers.

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