Circles: Area and circumference

Circles: Area and circumference

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Circles: Area and circumference

In a nutshell

All circles have a diameter and a radius. In combination with the Greek letter π\pi, these properties can be used to calculate the area and perimeter of a circle. 

Diameter and radius

The diameter is a straight line from one side of a circle to another which passes through the centre. The radius is a straight line from the centre of a circle to its side. 

The radius and diameter are linked by the formula:

 d=2rd = 2r​​

Where rr​ is the radius of the circle, and dd​ is the diameter.

Example 1

What property of a circle is shown by the line OAOA?

Maths; Shapes; KS3 Year 7; Circles: Area and circumference

The line passes from the centre of a circle to a point on the side labelled AA.

This defines the radius.

The line OA is the radius of the circle.


Circumference of a circle

The circumference is the name given to the perimeter of the circle. The Greek letter π\pi​ is a constant ratio between the circumference of a circle and its diameter.

The circumference of a circle is given by:

Circumference=2πr=πdCircumference=2\pi r = \pi d​​

π3.142\pi \approx 3.142​​

Note: The value of π\pi on a calculator can be used which will be more accurate. 

Example 2

What is the circumference of a circle which has a radius of 3cm3cm? Leave your answer in terms of π\pi.

Use the radius to calculate the diameter. 

2×3=6cm2 \times 3 = 6cm​​

Multiply the diameter by π\pi.

6×π=6π cm\underline{6 \times \pi = 6\pi \ cm}​​

Note: Remember to maintain the units throughout the question. 

Area of a circle

The area of  circle is the size of its surface. 

The area is given by the formula:

Area=πr2\text{Area}=\pi r^2​​

Example 3

The circle below has a radius of 5cm5cm.  What is the area in terms of π\pi?

Maths; Shapes; KS3 Year 7; Circles: Area and circumference

Identify the formula for the area of a circle.

Area=πr2{Area}=\pi r^2​​

Use the formula to calculate the area. 

Area=52×π{Area}=5^2 \times \pi ​​

Area=25π cm2\underline{{Area}=25\pi \ cm^2 }

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FAQs - Frequently Asked Questions

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