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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