The Circle

1
The Circle
Main Parts of a Circle
Investigation of the Ratio of Circle
Circumference of the circle
Composite shapes Perimeter
Diameter Circumference p
Area of a circle
Composite Area
2
Starter Questions

7cm
3
Main Parts of a Circle
Learning Intention
Success Criteria

1. To revise the basics of the circle.

• 1. Know the terms circumference, diameter and
  radius.
• 2. Identify them on a circle.
• 3. Calculate the circumference using formula.

4
Main part of a Circle
Main parts of the circle
O
5
Main part of a Circle
2cm
10cm
6
Main part of a Circle
Now try Exercise 1 Ch9 (page 100)
7
Starter Questions

5cm
8
Stars In Your Eyes
Today Matthew we are going to be

Archimedes of Syracuse
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History of Circles
75 years old
The Greek mathematician Archimedes of Syracuse (28
7- 212 BC) who flourished in Sicily is generally
considered to be the greatest mathematician of
ancient times. He is credited with determining
the relationship between the diameter and the
circumference of a circle. This was first
recorded by Archimedes in the book Measurement
of a Circle (225 BC). In this investigation we
are going to attempt to follow Archimedes
steps and arrive at the equation for determining
the circumference for any given circle.
10
Parts of the Circle
O
O centre of circle
11
Circle Investigation

• Construct a table shown below to enable us
• to record our results.

12
Investigation of the Circle
Our Investigation
To find a relationship between the diameter and
circumference of a given circle.
Question ?
How can we measure the diameter and circumference
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Measuring the Diameter of a circle
O
The diameter is the largest distance between one
side of a circle to the other passing through
the centre O.
14
Measuring the Circumference of a circle
15
Measuring the Circumference of a circle
Roll along an even surface
One complete rotation equals the length of the
circumference
Be careful to avoid slip!
16
Circle Investigation
17
Circle Investigation

• Using your results write down, in your own
  words,
• an approximate relationship between the
• circumference and diameter for a given circle.

Circumference approximately equals three and bit
diameters Actual value is 3.14 which we write as
p
Pronounced Pi
18
Circle Investigation
No Exercise
19
Starter Questions
4
20
Main Parts of a Circle
Learning Intention
Success Criteria

1. To revise the basics of the circle.

• 1. Know the terms circumference, diameter and
  radius.
• 2. Identify them on a circle.
• 3. Calculate the circumference using formula.

21
Main Parts of a Circle
Main parts of the circle
O
22
Calculating the Circumference
Example Find the length of the circumference
(Perimeter) of each circle
2cm
10cm
23
Calculating the Circumference
Q. Calculate the curved part of this shape.
6m
90o
24
Main part of a Circle
Now try Exercise 2 Ch9 (page 100)
25
Starter Questions
4
26
Composite Perimeter
Learning Intention
Success Criteria

1. Recall knowledge of circles so far.

1. To give some examples of problems that we
can solve by applying our knowledge of circles
and of the course so far.
2. Solve mixed problems by applying all our
knowledge so far.
27
Composite Perimeter
Things to think about when doing exercise.
The perimeter of a semicircle . Find whole
circle then half it !
The perimeter of a quarter circle . Find whole
circle then quarter it !
Composite perimeter . Find each perimeter and
add them together !
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Composite Perimeter
Q. Find the perimeter for the semi-circle shape ?
Solution
180o
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Composite Perimeter
Q. Find the perimeter of the shape below ?
8cm
90o
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Composite Perimeter
Example 1 Find the perimeter of this shape
Perimeter 3 sides semicircle
31
Composite Perimeter
Now try Extension Booklet 6E (page 125)
32
Starter Questions
33
Finding the Diameter
The Circle
Learning Intention
Success Criteria

1. Understand how to rearrange circumference formula
   to find diameter.

1. To explain how we can find diameter of a
circle if we know the circumference.
2. Solve diameter problems.
34
Finding the Diameter
The Circle
We can easily rearrange the circumference
formula so that we have the diameter D on one
side.
You have 1 minute to rearrange equation.
Remember change side change sign
35
Finding the Diameter
The Circle
Example Find the diameter of each circle given
the circumference.
C 62.8 cm
C 15.7 cm
5cm
20cm
36
Finding the Diameter
Now try Extension Booklet 4E (page 32)
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Starter Questions
38
Area of a Circle
A
circumference
A
B
x
x
O
O

• What do we call the distance OA in terms of
• the large circle.

• What do we call the distance AB in terms of
  the large circle.

39
Area of a Circle

• What is the formula for the area
• of a right-angle triangle.

• Use this formula to work out
• the area for a circle.

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Area of a Circle
41
Area of a Circle
42
Area of a Circle
But the area inside this rectangle is also the
area of the circle
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Area of a circle
Q. Find the area of the circle ?
4cm
44
The Area of a circle

• The area of a circle is 12.64 cm2.
• Find its radius?

45
Area of a circle

• The diameter of the circle is 60cm.
• Find area of the circle?

46
Area of a Circle
Now try Extension booklet 5E (page 35)
47
Starter Questions
48
Composite Area
Learning Intention
Success Criteria

1. Recall knowledge of circles so far.

1. To give some examples of problems that we
can solve by applying our knowledge of circles
and of the course so far.
2. Solve mixed problems by applying all our
knowledge so far.
49
Composite Area
Example 1 Find the area of the shape
Area rectangle semicircle
50
Composite Area
Example 1 Find the area of the red part.
Area Big Circle Small Circle
4cm
10cm
51
Composite Area
Example 2 A circle is contained in a
square. Find the grey shaded area below.
Area square - circle
8cm
52
Composite Area
Now try Extension booklet 6E (page 38)