Introduction to circles

1
The Circle
Introduction to circles
Lets investigate Circumference
Circumference examples
www.mathsrevision.com
Area of a circle
Area examples
2
Main part of a Circle
Learning Intention To identify the main parts of
a circle.

• Success Criteria
• Know the terms circumference, diameter and
  radius.
• Identify them on a circle.
• Calculate the circumference using formula.

www.mathsrevision.com
3
Main part of a Circle
Main parts of the circle
O
C 2pr
4
Lets investigate
We can use a ruler to measure the diameter.
How can we measure the circumference?
www.mathsrevision.com
Ask your teacher for the circles worksheet.
5
Lets investigate
circumference diameter
circumference diameter is roughly
There isnt an exact answer for this. It
actually goes on forever!
In 1989 a computer worked it out to 480 million
decimal places.
www.mathsrevision.com
3.141592653589793238462643383279502
Well stop here since it would stretch for 600
miles if we printed them all!
6
The Circumference
If it goes on for ever how can I write it down?
Mathematical Genius!
www.mathsrevision.com
This is called pi.
7
The Circumference
So circumference diameter
3.1415926535
By re-arranging this we get

x diameter
Circumference
www.mathsrevision.com
d
C
2 r
C
8
The Circumference
Some calculators have a button like this
www.mathsrevision.com
3.141592654
9
Example 1
C 2pr
C 2xpx3
C 6p cm
6cm
C 18.8cm (1 d.p.)
www.mathsrevision.com
What is the circumference of this circle?
10
Example 2
C 2pr
10cm
C 2xpx5
10cm
C 31.4cm (1 d.p.)
5cm
www.mathsrevision.com
What is the circumference of this circle?
11
The Circumference
Go back to the Circles worksheet and use the
formula to work out the circumference of each
circle.
www.mathsrevision.com
12
Area of a circle
Mathematical Genius!
www.mathsrevision.com
To find the area we could try counting the
squares inside the circle
There is a much more accurate way!
13
Area of a circle
There is a special formula for the area of a
circle.
www.mathsrevision.com
Remember r² means r x r
14
Example 1
4m
A 16p m²
A 50.3m² (1 d.p.)
www.mathsrevision.com
What is the area of this circle?
15
Example 2
Dont forget!
r
½ x 14
7cm
?
7cm
A 49p cm²
14cm
A 153.9cm² (1 d.p.)
www.mathsrevision.com
What is the area of this circle?
16

Example 3
Dont forget!
r
½ x 24
12m
?
12m

A 452.4m² (1 d.p.)
What is the area of this semi-circle?
Area of semi-circle
www.mathsrevision.com
½ x 452.4
226.2m²
A semicircle is half a circle.
First work out area of full circle.