Circles: Area and circumference

In a nutshell

All circles have a diameter and a radius. In combination with the Greek letter $\pi$ , 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:

$d = 2r$

Where $r$ is the radius of the circle, and $d$ is the diameter.

Example 1

What property of a circle is shown by the line $OA$ ?

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 $A$ .

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 $\pi$ is a constant ratio between the circumference of a circle and its diameter.

The circumference of a circle is given by:

$Circumference=2\pi r = \pi d$

$\pi \approx 3.142$

Note: The value of $\pi$ 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 $3cm$ ? Leave your answer in terms of $\pi$ .

Use the radius to calculate the diameter.

$2 \times 3 = 6cm$

Multiply the diameter by $\pi$ .

$\underline{6 \times \pi = 6\pi \ cm}$

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:

$\text{Area}=\pi r^2$

Example 3

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

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

Identify the formula for the area of a circle.

${Area}=\pi r^2$

Use the formula to calculate the area.

${Area}=5^2 \times \pi$ 

$\underline{{Area}=25\pi \ cm^2 }$