Shape and Space - part 1
CIRCLES - CIRCUMFERENCE A
The diameter of a circle is the

distance across it through the centre.

The radius is the distance from
the centre to the edge.

The circumference is the distance 
around the edge of the circle

Finding the circumference
If you measure the diameter of any circle, then measure around the
circumference, you’ll find that the circumference is just over 3 times
bigger than the diameter.
22cm
Try checking this with a
measuring tape
This number, the number of times
the diameter is multiplied by to find
the circumference, has the name π (a Greek letter pronounced like ‘pie’)
f lex i p
π is usually given the value 3.14 or
3.142 but if you press the EXP button
on a scientific calculator, you’ll see a
more accurate value (in fact it goes on
forever).
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7cm

Shape and Space - part 1
So to find the distance round the edge of any circle, multiply the
diameter by π.
The formula is:
C =πd


circumference
diameter
(The multiplication sign is not used in formulae, so C = π d means
C = π x d)
Example:
The circular pond is 4m wide. What is the distance around the edge?
Take the value π = 3.14
C
=
=
=
πd
3.14 x 4 m
12.56m
4m
A)
Try these using the value π = 3.14
1)
Find the circumference of these circles:
a)
b)
2cm
c)
d)
5cm
7cm
9cm
A circular teepee tent is 3m across the base. What is it’s
circumference?
3)
A vinyl LP record has a diameter of 30cm. What is the distance
around the edge?
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2)
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Shape and Space - part 1
4)
A hula hoop is 90cm across. What length of plastic is needed to
make it?
5)
Anne is completing an order for birthday cakes. How much
ribbon is needed to go round a cake 25cm wide?
6)
A circular rug is 95cm across. What length of binding is needed
to go round the edge?
π may be given as
22
7
(3
1
7
). In this case, work out the value as a
fraction and cancel if possible
Example:
22
Find the circumference of this circle, using the value π = 7
3
22
x 21 (cancel by 7)
7
1
21cm
= 22 x 3 cm
= 66cm
B)
More questions
Find the circumference using the value π =
1)
2)
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49cm
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3)
4)
35m
14m
3
22
7
105m
Shape and Space - part 1
Radius and diameter
Sometimes you may be given the radius instead of the diameter.
d
r
To find the diameter, just multiply the radius by 2
C =πd
C)
Try these questions using the value π = 3.142
1)
Find the circumference of these circles:
a)
b)
c)
4m
2)
6m
7m
The minute hand on a clock reaches to the edge, and is 5cm long.
What distance does the tip of the hand travel in an hour?
5cm
3)
A cow is tethered on the end of a rope 10m long, attached to a
fixed post. How far can she walk round in a circle?
10m
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Check your answers then discuss with your tutor what you need to
work on next.
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Shape and Space - part 1
Answers
Circles - Circumference A
A)
1)
a) 6.28cm
2)
9.42m
3)
94.2cm
4)
282.6cm
5)
78.5cm
6)
298.3cm
b) 15.7cm
c) 21.98cm
b) 37.704m
c) 43.988m
B)
1)
154cm
2)
44m
3)
110m
4)
330m
C)
a) 25.136m
2)
31.42cm
3)
62.84m
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1)
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d) 28.26cm
Shape and Space - part 1
CIRCLES - CIRCUMFERENCE B
Recap: C = π d
You may need to find the circumference of part of a circle, or a split
circle.
Example:
What is the length of the
curved edge of this fan?
7cm
First let’s find the whole circumference:
Radius = 7cm so diameter = 14cm
C = πd
= 14 x 3.14 cm
= 43.96cm
The curved edge is only a quarter circle, so divide by 4
43.96
Curved edge =
4
= 10.99cm
Try these examples:
1)
What is the length of the curve in this goal
area?
2)
14m

10m
5m
What is the total length
around the outside of this
running track?

(HINT: You have a complete circle and 2 straight sections)
3)
How far would you run
in a lap on this track?
20m

15m

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Check your answers then discuss with your tutor what you need to
work on next.
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Shape and Space - part 1
Answers
Circles -Circumference B
7.855 m
2)
59.4 m
3)
87.1 m
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1)
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Shape and Space - part 1
CIRCLES - CIRCUMFERENCE C
If you already know the length of the circumference of a circle, you
can work back to find the diameter.
The diameter was multiplied by π to find the circumference - so to
get back to the diameter:
Just divide the circumference by π
d =
c
π
Example:
The distance round the edge of this
pond is 35 metres.
What is the diameter?
(π = 3.14)
d
=
c
π
=
35
3.14
Using a calculator
= 11.15cm (to 2 decimal places)
A)
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1)
Try these: Take π as 3.14 and give the answer to 2 d p
An infant school sports track needs to have a circumference of
100m. What should:
a) the diameter
b) the radius be?
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Shape and Space - part 1
2)
A circular athletics track for a junior school has to be 400m long.
What will:
a) the diameter
b) the radius be?
3)
Ben is making a circular flower garden, using 36 metres of stone
edging for the border.
a) What is the greatest diameter the garden can have?
b) What radius would he need to draw?
22
, the formula will look like this:
7
c
22
d=
which can be written d = c 
π
7
If π is given as 3
1
7
or
Remember when you divide fractions, the number you are dividing by
is turned upside down.
7
22
So
d = cx
B)
Try these:
Find a) the diameter
22
using π =
7
b) the radius of these circle
circumference
circumference
circumference
44m
121m
5.5m
1)
2)
3)
circumference
1
162 miles
4)
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Check your answers then discuss with your tutor what you need to
work on next.
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Shape and Space - part 1
Answers
Circles - Circumference C
A)
1)
a) 31.85 m
b) 15.93 m
2)
a) 127.39 m
b) 63.70 m
3)
a) 11.46 m
b) 5.73 m
B)
a) 14 m
b) 7 m
2)
a) 38.5 m
b) 19.25 m
3)
a) 1.75 m
b) 0.875 m
4)
a) 5.25 miles
b) 2.625 miles
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1)
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Shape and Space - part 1
CIRCLES - CIRCUMFERENCE D
Example:
The circumference is the distance a wheel travels in one turn
30cm


This wheel has a diameter of 30cm. After one turn it has gone the
length of the circumference.
314
x30
9420
C =πd
= 3.14 x 30
= 94.2cm
=94.2 (there are 2
decimal places)
How many turns will it make if it travels 10 metres?
10 metres = 1000cm
1000cm  94.2 = 10.6 (to 1 decimal place)
Answer: it will make 10 complete turns.
Try these questions using the value π = 3.14
1)
A tractor tyre measures 1m across.
How far does it travel in one turn?
How many complete turns does it make in 1 kilometre?
2)
A Lego tractor wheel measures 2 cm across.
How far does it travel in one turn?
How many complete turns does it make in 1 metre?
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Check your answers then discuss with your tutor what you need to
work on next.
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Shape and Space - part 1
Answers
Circles - Circumference D
3.14 m
318 turns
2)
6.28 cm
15 turns
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1)
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