The Circle
1.
2.
3.
4.
Thursday, 24 March 2016
Know the names of a circle’s features
Calculate the circumference
Calculate an arc length
Deal with the revolution of wheels and
journey problem
Why am
Levels 5  8
I doing
this?
A wheel is a circle!
OK Circles in design – Mickey
What
Mouse is made from circles
have
I
got
A real favourite SAT and
to do?
GCSE question
Circle Starter
Level 5
Name these Features
The distance from the
centre to the edge
The distance from one side
to the other passing through
the centre
The distance all of the way
round the edge
The blue line
Area Circumference Rotation Radius
Degree Chord Sector Segment Diameter
Sphere Concentric Arc
The distance from the centre to
the edge RADIUS
Segment
Sector
The distance from one side to the
other passing through the centre
DIAMETER
The distance all of the way round
the edge CIRCUMFERENCE
An ARC is the name
for part of the
circumference
The blue line CHORD
Where can you see i) a segment
ii) a sector iii) an arc?
APPROXIMATELY
FINDING THE
CIRCUMFERENCE
Level 5
APPROXIMATELY what is
the relationship (connection)
between a circle’s diameter
and its circumference?
To APPROXIMATELY find the
CIRCUMFERENCE MULTIPLY the
DIAMETER by 3 (C = 3 x d)
Radius
Diameter
4
8
Circumference
12
10
5
15
18
30
42
To APPROXIMATELY find the
CIRCUMFERENCE MULTIPLY the
DIAMETER by 3 (C = 3 x d)
Radius
2
4
Diameter
4
8
Circumference
12
24
6
10
5
12
20
10
36
60
30
15
3
5
7
30
6
10
14
90
18
30
42
SAT Aural Question ( Answer
a question in 10 seconds)
• A circle has a diameter of
10 cm. APPROXIMATELY
(ROUGHLY), what is its
circumference? 30
• A circle has a
cm
circumference of 18 cm.
Approximately, what is its
diameter?
6 cm
Calculate the
Circumference
Using the Correct
Formula
Level 6
How to calculate the circumference
Evaluate the
CIRCUMFERENCE
Diameter = 12 cm
C=
d
Always, write
the formula
(rule)
C = 3.14 X 12
C = 37.68
The
symbol is the Greek
letter pi. It stands for a number
that can never be found
exactly. It is approximately
3.14
How to calculate the diameter from the
circumference
If the
circumference is 40
cm. evaluate the
DIAMETER
Diameter = ?cm
C=
d
Always, write
the formula
(rule)
d=C÷
d = C ÷ 3.14
d = 40 ÷ 3.14
d = 12.73
1
2
3
4
5
6
7
8
9
10
Diameter
24
14
Radius
Circumference
17
30
22
120
78
88
Remember
d=2Xr
r=d÷2
120
340
1
2
3
4
5
6
7
8
9
10
Diameter
24
14
34
60
22
120
156
176
38.22
108.28
Radius
12
7
17
30
11
60
78
88
19.11
54.14
Circumference
75.36
43.96
106.76
188.4
69.08
376.8
489.84
552.64
120
340
Calculate an
Arc Length
Level 7
How to Calculate an Arc
Calculate the arc length
Length
AB for a circle with a
A
diameter of 12 cm.
720
B
Circumference
C = 3.14 x 12
C = 37.6 cm
But we only want the arc length
AB. This is 720 of the circle
and because there are 3600 in a
circle, this is 72 ÷ 360 = 0.2 as
a decimal fraction of the
circumference
AB = 0.2 x C
AB = 0.2 x 37.6
AB = 5.52
The FORMULA for an
Arc Length A
Calculate the arc length
AB for a circle with a
diameter of
x0
d
AB = x/360(
B
d)
AB = (x ÷ 360) x 3.14 x d
Divide the arc length’s angle
by 360 then multiply this by
the circumference
Using the FORMULA for
Calculate the arc length
an Arc
AB for these circles
A
x0
1.
2.
3.
X0
144
48
180
AB = x/360(
d)
B AB = (x ÷ 360) x 3.14 x d
Diam Arc AB
12
40
25
4.
5.
6.
X0
270
24
70
Diam Arc AB
60
36
40
Using the FORMULA for
Calculate the arc length
an Arc
AB for these circles
A
x0
1.
2.
3.
X0
144
48
180
AB = x/360(
d)
B AB = (x ÷ 360) x 3.14 x d
Diam Arc AB
12
15.07
40
20.10
25
39.25
4.
5.
6.
X0
270
24
70
Diam Arc AB
60
141.3
36
7.54
40
24.42
Finding the Number
of Revolutions
(turns) of a Wheel on
a Journey
Level 8
A wheel with a spot
of blue paint
The wheel turns once
This distance is the circumference
When a wheel makes one complete
revolution, the distance that it
travels is its circumference
How many times will a wheel with a diameter of 0.5
metre rotate when it travels distance of 100 metres?
100 metres
1.57
When a wheel
makes one
complete
revolution, the
distance that
it travels is its
circumference
1. Find the
circumference of the
wheel
C = 3.14 x 0.5
C = 1.57
2. Divide this into 100 to
find the number of
revolutions
Revs = 100 ÷ 1.57
Revs = 63.7 times
1. Find the circumference of the wheel
C = 3.14 x d
2. Divide this into the journey to find the
number of revolutions
Revs = Journey Distance ÷ C
Wheel’s Circumference Distance of Number of
Diameter
Journey
Revolutions
0.3 metres
120 metres
0.4 metres
200 metres
0.7 metres
150 metres
0.6 metres
1000 metres
Wheel’s Circumference Distance of Number of
Diameter
Journey
Revolutions
0.3 metres
120 metres
0.4 metres
200 metres
0.7 metres
150 metres
0.6 metres
1000 metres
A bike’s wheels have a
diameter of 70 cm.
How many times will
the wheel revolve
during a journey of 50
km?
Level 8
A car’s wheels have a
diameter of 45 cm.
How many times will
the wheel revolve
during a journey of 100
km?