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: \(\text{circumference} = \pi \times \text{diameter}\)
For any circle:
\(\text{circumference} \div \text{diameter} = 3.1412 \dotsc\)
This number is Pi (\(\pi\)). It is a number which goes on forever.
\(\pi = 3.1415926535897932384626433832795 \dotsc\)
Pi cannot be written as an exact fraction or decimal. Approximations can be used. A typical approximation is 3.14.
Scientific calculators have a \(\pi\) button which can be used instead of an approximation.
Example
Calculate the circumference of the dartboard.
The diameter is twice the radius.
\(d = 20 \times 2 = 40~\text{cm}\)
Circumference = \(40 \times \pi = 125.7~\text{cm}\)
The answer can also be given in terms of \(\pi\). In this case the answer is \(40 \pi~\text{cm}\).
The circumference formula can be used to solve problems.
Question
How many full rotations will the wheel make if it travels 3,500 cm?
Circumference of the wheel is: \(27.5 \times 2 \times \pi = 172.8~\text{cm}\)
In one rotation the wheel travels 172.8 cm.
To calculate the number of rotations:
\(3,500 \div 172.8 = 20.25\)
This is 20 full rotations.