CIRCLES I

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CIRCLES I
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radius
circumference
centre
tangent
diameter
chord
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Here are 2 mathematical statements.
The circumference of a circle is less than 4
times its diameter
The circumference of a circle is more than 3
times its diameter
Which statements do you think are true?
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perimeter of circle
perimeter of square
perimeter of hexagon


Lets use a diagram to help
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C
4d
8r
6r
3d
Both statements are true
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A group of students measured the radius
diameter of six circles to see how they were
related. Here are their results
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Here is their graph
The equation of the line is d 2r
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A group of students then measured the
circumference of the circles and compares these
measurements with the diameters.
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The equation of the line is d 3.1 r
Here is their graph
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From their experiment, the students concluded
that radius, diameter and circumference of any
circle are all closely related as follows.
d2
d 2r
r
C 2 x 3.1 x r
C 3.1
d
C 3.1 x d
How many diameters make a circumference?
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Mathematicians have always been fascinated by the
number of diameters that make a circumference
The Ancient Babylonians (2000BC) believed the
number to be 3 and an eighth
By 1660, Newton had calculated it to 16 decimal
places
Archimedes calculated it as 3.1418
By 1997, the number had been calculated to
400,000,000, 000 decimal places
This number has a name
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p
13
p x d
C pd
C 2pr
2 x p x r
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This circle has a diameter of 10 cm.
Find the radius circumference of the circle
10 cm
Use p 3.14
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d2
Radius
10 cm
10 2

5 cm

pd
circumference

p x 10


3.14 x 10
31.4 cm
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Calculate the perimeter of this semicircle
Use p 3.14
12 m
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Calculate the perimeter and area of this
semicircle
Use p 3.14
12 m
pd2
Perimeter
d
(3.14 x 12) 24
37.68 24
61.68 m
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End