Introduction to circles

Let’s investigate… Circumference

Circumference examples

The CircleThe Circle

Starter Questions Starter Questions

1. What shape has an infinte line symmetry.

2. Write down 5 everyday objects that are

in the shape of a circle.

3. Find the perimeter of the star.

4. Convert your answer to Q3 to (m).

7cm

Main parts of the circle

Main part of a CircleMain part of a Circle

radius

O

Circumference Diameter2D r

12

r D

C D

Let’s investigate…

We can use a ruler to measure the diameter.

How can we measure the circumference?

3.141592653589793238462643383279502…

Let’s investigate…Look at the column

circumference ÷ diameter

circumference ÷ diameter is roughly

There isn’t an exact answer for this. It actually goes on forever!

We’ll stop here since it would stretch for 600

miles if we printed them all!

In 1989 a computer worked it out to 480 million decimal places.

3

Let’s Investigate...Let’s Investigate...

Circular Item Circumference

Diameter Π

The CircumferenceIf it goes on for ever

how can I write it down?

We use the Greek letter

instead.

MathematicalGenius!

This is called pi.

3.1415926535So circumference ÷ diameter =

Circumference =

x diameter

By re-arranging this we get:

C =

d

The Circumference

This button stores to 8 or 9 decimal places which is more than accurate enough!

3.141592654

When doing circle calculations, you will normally use a calculator.

Some calculators have a button like this:

If your calculator doesn’t haveThen use 3.14 instead.

The Circumference

Example 1

6cm

What is the circumference of this circle?

C = dC = x 6

Press

Then x 6 =

C = 18.8cm (1 d.p.)

Example 2

5cm

What is the circumference of this circle?

C = d

C = x 10

Remember: diameter = 2 x

radius

C = 31.4cm (1 d.p.)

d = 2 x 5 = 10cm

10cm

Go back to the Circles worksheet and use

to work out the circumference of each

circle.

C =

d

The Circumference

Area of a circle

To find the area we could try counting the squares inside the circle…

1

2 3 4

5 6 7

8

?

?

? ?

? ?

?

?

There is a much more accurate

way!

MathematicalGenius!

Area of a circle

A = r²

Area =

x radius

x radius

There is a special formula for the area of a circle.

Remember:r² means r x

r

Example 1

What is the area of this circle?

A = r²A = x 4 x 4

Press

Then x 4 x4 =

A = 50.3m² (1 d.p.) 4m

Example 2

What is the area of this circle?

A = r²

A = x 7 x 7

Press

Then x 7 x 7 =

A = 153.9cm² (1 d.p.) 14cm

?7cm

r = ½ x 14 = 7cm Don’tforget!

24m

Example 3

What is the area of this semi-circle?

A = r²

A = x 12 x 12

A semicircle is half a circle.

A = 452.4m² (1 d.p.)

?12m

r = ½ x 24 = 12m Don’tforget!

Area of semi-circle

= ½ x 452.4

First work out area of full

circle.

=226.2m²