Introduction to circles

1
The Circle
Introduction to circles
Lets investigate Circumference
Circumference examples
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.

3
Main part of a Circle
Main parts of the circle
O
4
Lets investigate
We can use a ruler to measure the diameter.
How can we measure the circumference?
5
Lets investigateWork as a team at your table

1. Cut a piece of yarn that is exactly the length of
   the distance around the circular object at your
   table. (Called the circumference)
2. Cut another piece of yarn that is exactly the
   length of the distance through the middle of your
   circular object. (Called the diameter)
3. Use a ruler (in cm) to measure these two pieces
   of string. Be as accurate as possible!
4. Use a calculator to divide the Circumference by
   the diameter.

6
Lets investigate
Look at the column circumference diameter
circumference diameter is roughly
7
Lets investigate
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.
3.141592653589793238462643383279502
Well stop here since it would stretch for 600
miles if we printed them all!
8
The Circumference
If it goes on for ever how can I write it down?
Mathematical Genius!
This is called pi.
9
The Circumference
So circumference diameter
3.1415926535
By re-arranging this we get

x diameter
Circumference
d
C
10
The Circumference
Some calculators have a button like this
3.141592654
11
Example 1
6cm
C 18.8cm
What is the circumference of this circle?
12
Example 2
d
2 x 5
10cm
10cm
C 31.4cm
5cm
What is the circumference of this circle?
Remember diameter 2 x radius
13
Area of a circle
Mathematical Genius!
To find the area we could try counting the
squares inside the circle
There is a much more accurate way!
14
Area of a circle
There is a special formula for the area of a
circle.
Remember r² means r x r
15
Example 1
4m
A 50.3m²
What is the area of this circle?
16
Example 2
Dont forget!
r
½ x 14
7cm
7cm
?
A 153.9cm²
14cm
What is the area of this circle?
17
Example 3
Dont forget!
r
½ x 24
12m
?
12m

A 452.4m²
What is the area of this semi-circle?
Area of semi-circle
½ x 452.4
226.2m²
A semicircle is half a circle.
First work out area of full circle.
18
Joke of the Day!
What do you get when you take the circumference
of an apple and divide it by the diameter of the
apple?
Apple Pi!