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1. October 4, 2012
Circles
1. Circumference, diameter and radius.
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2. Explanation October 4, 2012
Here is a circle.
chord
r
mete
dia ra
arc
di
us
tange
n t
Part straight line a straight is anthrough the a does not
The diameter a the way round the to at circumference.
Any distance allline from the centre,perimeter is known
radius circumference linethe circle, but single from
of the is is that touches arc.
crosses circle centre, point
pass through tangent.
one side as athe centre, is known as a chord.
asknown to the other.
is the circumference.
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3. Explanation October 4, 2012
Jamal gathered together five circular objects.
He measured them, to find out how many times bigger
the circumference of each object was, compared to the
diameter. These are his results, in centimetres, to 1d.p.
Object circumference diameter circumference
diameter
Clock 77.6 25 3.1
Tin of Beans 26.6 8.4 3.2
Biscuit tin 98.9 34 2.9
Can of Lilt 22.1 7.2 3.1
Airfix pot 5.5 1.7 3.2
Jamal was surprised to discover that no matter what size
the object he measured, the circumference of the object
was always about three times bigger than the diameter.
This approximate relationship can be written C ~ 3 × d
~
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4. Explanation October 4, 2012
People have known for thousands of years that that the
ratio of the circumference to the diameter of a circle is
constant.
Accurate measurements have shown the circumference
to be approximately 3.142 × the diameter, but in actual
fact the number is never ending and does not show any
recurring pattern. This makes it an irrational number.
As an irrational number, we use a Greek letter to denote
it. That letter is π, or pi, so,
C = π × d or C = π d
If you know the radius, rather than the diameter, then
C = π × 2r or C = 2π r
Your calculator will have a button for the value of π. π
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5. Example October 4, 2012
As pi is such a long number, you need to write your
answers to a small number of decimal places.
A circle has a diameter of 16cm. 16cm
What is its circumference?
Circumference = πd
= π × 16
= 50.2654825…
50.3cm, to 1 d.p.
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6. Example October 4, 2012
As pi is such a long number, you need to write your
answers to a small number of decimal places.
A circle has a radius of 7cm. 7cm
What is its circumference?
Circumference = 2πr
= 2 × π × 16
= 43.9822972…
44.0cm, to 1 d.p.
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7. Example October 4, 2012
You can also work out the diameter, or radius of a circle,
if you know the circumference.
A circle has a circumference of 18m.
18m
What is its diameter?
C = πd
20 = π d
To find d, divide d=
both sides by π
6.366197…
The diameter of the circle is 6.37m, to 2 d.p.
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