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Maths

Circles

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# Circumference of a circle

The circumference is the length of the edge around a circle.

For any circle, the circumference is:

3.141592... × the diameter.

Or in symbols: C = (3.141592...)d

This is true for all circles and so 3.141592... is therefore a special, unique number, and we represent it with the Greek letter π.(The symbol π is called 'pi' in English and is pronounced 'pie').

So we can write the formula for the circumference of a circle as: C = πd

However, the diameter is equal to 2 × radius, (2r), so we can also write this formula as:

C = 2πr

It does not matter which of these formulae you use. But you must be careful to use the correct length for the formula (the radius or diameter).

Look at the following example:

Question

Find the circumference of a wheel with a diameter of 50 cm. Use π = 3.14.

Solution 1: Using C = πd

We know that the diameter is 50 cm, so we simply calculate:

πd = 3.14 × 50 = 157 cm

Solution 2: Using C = 2πr

We have been given the diameter (50 cm), so we must start by finding the radius. The radius is half the diameter, so the radius is 25 cm.

2πr = 2 × 3.14 × 25 = 157 cm

Question

A plate has a radius of 15 cm. Find the circumference by using the π button on your calculator, and give your answer correct to 1 decimal place (dp).

Solution 1 : Using C = πd

We must first calculate the diameter:

d = 2r, so d = 2 × 15 = 30 cm

C = π × 30 = 94.2477...

C = 94.2 cm (1 d.p.)

Solution 2 : Using C = 2πr

C = 2 × π × 15 = 94.2477...

C = 94.2 cm (1 dp)

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