# The Circle Introduction to circles www mathsrevision com Let’s investigate… Circumference

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```					                              The Circle

Introduction to circles
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Let’s investigate… Circumference
Circumference examples
Area of a circle
Area examples
Starter Questions

1. What shape has an infinte line symmetry.
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2. Write down 5 everyday objects that are
in the shape of a circle.
7cm
3. Find the perimeter of the star.

Main part of a Circle

Learning Intention
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To identify the main parts of a circle.

Success Criteria

1. Know the terms circumference, diameter
2. Identify them on a circle.
3. Calculate the circumference using
formula.
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Main part of a Circle

Main parts of the circle
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1
r  D
2
O

Circumference                               Diameter
C  D                                       D  2r
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Starter Questions

2
Q1.   Calculate     66 % of £270
3
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Q2.   Convert 60% to fraction and simplify.

4
Q3.   Convert       to a percentage.
5
Q4.   What is the time difference 09:28 and 10:50

Q5.   The answer to the question is 90. What is the
question.

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Let’s investigate…

We can use a ruler to measure the diameter.

How can we measure
the circumference?

the circles worksheet.
Let’s investigate…
Look at the column
circumference ÷ diameter

circumference ÷ diameter is roughly     3
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There isn’t an exact answer for this.
It actually goes on forever!
In 1989 a computer worked it out to 480 million
decimal places.
3.141592653589793238462643383279502…
We’ll stop here since it
would stretch for 600 miles
if we printed them all!
The Circumference

If it goes on for ever how
can I write it down?
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
Mathematical
Genius!                   We use the Greek
letter

This is called pi.
The Circumference

So circumference ÷ diameter =
  3.1415926535
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By re-arranging this we get:

Circumference =              x diameter

C=       d
Starter Questions

Q1.   Tidy up the expression                2y+3x+4x+10
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2
Q2.   Calculate     of 84
3
Q3.   Round to 1 decimal place.

(a)   2.34 (b)         10.25 (c)           3.23

Q4.   12.5 % as a fraction

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The Circumference

When doing circle calculations, you
will normally use a calculator.
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Some calculators have a button like this:   
This button stores    to 8 or 9 decimal places
which is more than accurate enough! 3.141592654

doesn’t have   
Example 1
C=d
C= x6
6cm
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C = 18.8cm (1 d.p.)

What is the
circumference of
Press    
this circle?
Then x   6=
Example 2
C=   d
d = 2 x 5 = 10cm

 x 10
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10cm          C=
5cm          C = 31.4cm (1 d.p.)

What is the
circumference of     Remember:
this circle?       diameter = 2 x
The Circumference

Go back to the Circles
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worksheet and use
C=   d
to work out the
circumference of each
circle.
Starter Questions

1. Simplify a  4a  13d  11a  a  3d
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2. The ratio of apples to pears is 2 : 5.
If there are 28 pieces of fruit in total.
How many apples are there.

3.    What is the highest number that
divdes in 8 and 18 without leaving
a remainder.
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Area of a circle

?   1   ?
? 2     3   4 ?
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Mathematical
? 5 6       7 ?
Genius!                                ? 8       ?
To find the area we could try counting
the squares inside the circle…

There is a much
more accurate way!
Area of a circle

There is a special
formula for the
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area of a circle.


A=  
Remember:
r²

r² means r x
r
Example 1
A=  r²
A = x 4 x 4
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4m          A = 50.3m² (1 d.p.)

What is the area
Press   
of this circle?     Then x 4 x4 =
Example 2
A=    r²
Don’t
r = ½ x 14 = 7cm    forget!
?
7cm

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A=       x7x7
14cm            A = 153.9cm² (1 d.p.)

What is the area
Press   
of this circle?
Then x 7 x 7
=
Example 3
A=    r²
Don’t
r = ½ x 24 = 12m       forget!


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?
12m                 A=       x 12 x 12
24m
A = 452.4m² (1 d.p.)
What is the area of
this semi-circle?     Area of semi-circle
= ½ x 452.4 =226.2m²

First work out             A semicircle is
area of full circle.          half a circle.

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