Introduction to circles

1
The Circle
Introduction to circles
Lets investigate Circumference
Circumference examples
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Area of a circle
Area examples
2
Starter Questions

7cm
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3
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.

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4
Main part of a Circle
Main parts of the circle
O
5
Starter Questions
Q1. Calculate
Q2. Convert 60 to fraction and simplify.
to a percentage.
Q3. Convert
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Q4. What is the time difference 0928 and 1050
Q5. The answer to the question is 90. What is
the question.
6
Lets investigate
We can use a ruler to measure the diameter.
How can we measure the circumference?
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Ask your teacher for the circles worksheet.
7
Lets investigate
Look at the column 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.
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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!
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This is called pi.
9
The Circumference
So circumference diameter
3.1415926535
By re-arranging this we get

x diameter
Circumference
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d
C
10
Starter Questions
Q1. Tidy up the expression
Q2. Calculate
Q3. Round to 1 decimal place.
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(a) 2.34 (b) 10.25 (c) 3.23
Q4. 12.5 as a fraction
11
The Circumference
Some calculators have a button like this
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3.141592654
12
Example 1
6cm
C 18.8cm (1 d.p.)
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What is the circumference of this circle?
13
Example 2
d
2 x 5
10cm
10cm
C 31.4cm (1 d.p.)
5cm
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What is the circumference of this circle?
Remember diameter 2 x radius
14
The Circumference
Go back to the Circles worksheet and use to
work out the circumference of each circle.
d
C
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15
Starter Questions
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16
Area of a circle
Mathematical Genius!
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To find the area we could try counting the
squares inside the circle
There is a much more accurate way!
17
Area of a circle
There is a special formula for the area of a
circle.
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Remember r² means r x r
18
Example 1
4m
A 50.3m² (1 d.p.)
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What is the area of this circle?
19
Example 2
Dont forget!
r
½ x 14
7cm
?
7cm
A 153.9cm² (1 d.p.)
14cm
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What is the area of this circle?
20

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
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½ x 452.4
226.2m²
A semicircle is half a circle.
First work out area of full circle.