# Circles (basic)

Circles can be great fun and they are so easy to learn about. To understand circles we only need a few basic facts.

These are the ones you need to know.

Key facts

• Circumference = the distance around the edge of the circle.

• Diameter = a line across the widest part of a circle that passes through the centre.

• Radius = 1/2 the diameter. You can imagine that measuring the circumference of a circle can be tricky. We could use a piece of string and then put the string against a ruler to measure it.

There is a quicker way, can you remember?

Go

Yes we use the Diameter. We use this because it is easy to measure the diameter of a circle. It's not really tricky.

The diameter is ALWAYS approximately 3 times smaller than the circumference!

Or to put it another way, the circumference is approximately 3 times bigger than the diameter. Look at the table below and see if you can spot the pattern.

 Diameter Circumference Approx. 10 cm 31.4 cm 10cm X 3 = 30 2 cm 6.24 cm 2cm X 3 = 6 5 cm 15.7 cm 5cm X 3 = 15 cm

So you can see that multiplying the diameter by 3 gives us a very close answer.

To get the exact answer we have to multiply the diameter by 3.14. This number has got a special symbol and name

The name is PI (pie) and the symbol is π

So we could write the following:

A circumference of any circle is approx. 3 X the diameter.

If we want to be more accurate we could write:

A circumference of a circle is π x the diameter

In the next table try and calculate both the approximate circumference of a circle and the exact circumference.

Use a calculator if you wish.

The first one has been done for you

 Diameter Circumference(approx) Circumference 4 cm 12 cm 12.56cm 8 cm 20 cm 40 cm 3m 5 cm

 Diameter Circumference(approx) Circumference 4 cm 12 cm 12.56cm 8 cm 24 cm 25.12cm 20 cm 60 cm 62.8cm 40 cm 120 cm 125.6cm 3m 9m 9.42m 5 cm 15.7 cm 15.7cm

How did you do?

We have not yet talked about the radius. The radius is often more useful than the diameter and we will discuss that another day.

At the moment you only need to know that the radius is half the diameter. To put it another way the diamter is twice the radius.

# Look at the table

Look at the pattern

 Radius Diameter Circumference 1cm 2 cm 6.24cm 10cm 20cm 62.4cm 20cm 40cm 124.8cm

You see the radius is 1/2 the diameter and 1/6 the size of circumference.

Review

To find the circumference of a circle X the diameter by 3 to find the approx. size and 3.14 to find an accurate measure.

To find the radius of a circle divide the diameter by 2.

We will cover circle properties again later.

Good luck!