The Circle

1
The Circle
Tuesday, 22 December 2020

• Know the names of a circles features
• Calculate the circumference
• Calculate an arc length
• Deal with the revolution of wheels and journey
  problem
• Levels 5 ? 8

Why am I doing this?
A wheel is a circle! Circles in design Mickey
Mouse is made from circles A real favourite SAT
and GCSE question
OK - What have I got to do?
2
Circle Starter Level 5
3
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
4
The distance from the centre to the edge
RADIUS The distance from one side to the other
passing through the centre DIAMETER The distance
all of the way round the edge CIRCUMFERENCE The
blue line CHORD
Segment
Sector
An ARC is the name for part of the circumference
Where can you see i) a segment ii) a sector iii)
an arc?
5
APPROXIMATELY FINDING THE CIRCUMFERENCE
Level 5
6
APPROXIMATELY what is the relationship
(connection) between a circles diameter and its
circumference?
7
To APPROXIMATELY find the CIRCUMFERENCE MULTIPLY
the DIAMETER by 3 (C 3 x d)
Radius Diameter Circumference
4
8
12
10
5
15
18
30
42
8
To APPROXIMATELY find the CIRCUMFERENCE MULTIPLY
the DIAMETER by 3 (C 3 x d)
Radius Diameter Circumference
2 4 12
4 8 24
6 12 36
10 20 60
5 10 30
15 30 90
3 6 18
5 10 30
7 14 42
9

• SAT Aural Question ( Answer a question in 10
  seconds)
• A circle has a diameter of 10 cm. APPROXIMATELY
  (ROUGHLY), what is its circumference?
• A circle has a circumference of 18 cm.
  Approximately, what is its diameter?

30 cm
6 cm
10
Calculate the Circumference Using the Correct
Formula
Level 6
11
How to calculate the circumference
Evaluate the CIRCUMFERENCE
Always, write the formula (rule)
C d C 3.14 X 12 C 37.68
Diameter 12 cm
The symbol is the Greek letter pi. It
stands for a number that can never be found
exactly. It is approximately 3.14
12
How to calculate the diameter from the
circumference
Always, write the formula (rule)
C d d C d C 3.14 d 40 3.14 d
12.73
If the circumference is 40 cm. evaluate the
DIAMETER
Diameter ?cm
13
Diameter Radius Circumference
1 24
2 14
3 17
4 30
5 22
6 120
7 78
8 88
9 120
10 340

• Remember
• d 2 X r
• r d 2

14
Diameter Radius Circumference
1 24 12 75.36
2 14 7 43.96
3 34 17 106.76
4 60 30 188.4
5 22 11 69.08
6 120 60 376.8
7 156 78 489.84
8 176 88 552.64
9 38.22 19.11 120
10 108.28 54.14 340
15
Calculate an Arc Length
Level 7
16
How to Calculate an Arc Length
Calculate the arc length AB for a circle with a
diameter of 12 cm.
A
720
Circumference C 3.14 x 12 C 37.6 cm
B
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
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The FORMULA for an Arc Length
Calculate the arc length AB for a circle with a
diameter of d
A
x0
AB x/360( d) AB (x 360) x 3.14 x d
B
Divide the arc lengths angle by 360 then
multiply this by the circumference
18
Using the FORMULA for an Arc
Calculate the arc length AB for these circles
A
AB x/360( d) AB (x 360) x 3.14 x d
x0
B
X0 Diam Arc AB X0 Diam Arc AB
1. 144 12 4. 270 60
2. 48 40 5. 24 36
3. 180 25 6. 70 40
19
Using the FORMULA for an Arc
Calculate the arc length AB for these circles
A
AB x/360( d) AB (x 360) x 3.14 x d
x0
B
X0 Diam Arc AB X0 Diam Arc AB
1. 144 12 15.07 4. 270 60 141.3
2. 48 40 20.10 5. 24 36 7.54
3. 180 25 39.25 6. 70 40 24.42
20
Finding the Number of Revolutions (turns) of a
Wheel on a Journey
Level 8
21
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
22
How many times will a wheel with a diameter of
0.5 metre rotate when it travels distance of 100
metres?
100 metres

• 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

1.57
When a wheel makes one complete revolution, the
distance that it travels is its circumference
23

• 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

Wheels Diameter Circumference Distance of Journey Number of Revolutions
0.3 metres 120 metres
0.4 metres 200 metres
0.7 metres 150 metres
0.6 metres 1000 metres
24
Wheels Diameter Circumference Distance of Journey Number of Revolutions
0.3 metres 120 metres
0.4 metres 200 metres
0.7 metres 150 metres
0.6 metres 1000 metres
25
A bikes wheels have a diameter of 70 cm. How
many times will the wheel revolve during a
journey of 50 km?
A cars wheels have a diameter of 45 cm. How many
times will the wheel revolve during a journey of
100 km?
Level 8