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: \(\text{circumference} = \pi \times \text{diameter}\)
Pi (蟺)
For any circle:
\(\text{circumference} \div \text{diameter} = 3.1415 \dotsc\)
This number is Pi. It is a number which goes on forever.
\(\pi = 3.1415926535897932384626433832795 \dotsc\)
The pi symbol (\(\pi\)) 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 \(\pi\) button which can be used during calculations, with the final answer being rounded off as appropriate.
Example
Calculate the circumference of the dartboard.
The diameter is twice the radius.
\(d = 20 \times 2 = 40~\text{cm}\)
Circumference = \(40 \times \pi = 125.7~\text{cm}\) (1 decimal place).
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: \(27.5 \times 2 \times \pi = 172.8~\text{cm}\) (1 decimal place)
In one rotation the wheel travels 172.8 cm (or \(55\pi\)).
To calculate the number of rotations:
\(3,500 \div 172.8 = 20.25\) (or \(3500 \div 55\pi = 20.26)\).
This is 20 full rotations.