# 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 *$OA$*?*

*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 *$\pi$*?*

*Identify the formula for the area of a circle.*

${Area}=\pi r^2$

*Use the formula to calculate the area. *

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

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