the circle 1. know the names of a circle’s features 2. calculate the circumference 3. calculate an...
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The Circle1. Know the names of a circle’s features2. Calculate the circumference 3. Calculate an arc length4. Deal with the revolution of wheels and
journey problem
Levels 5 8
Wednesday 19 April 2023
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?
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
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
Where can you see i) a segment ii) a sector iii) an arc?
Sector
Segment
An ARC is the name for part of the circumference
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 Circumference
4
8
12
10
5
15
18
30
42
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
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
Calculate the Circumference Using the Correct Formula
Level 6
Diameter = 12 cm
C = d
C = 3.14 X 12
C = 37.68
How to calculate the circumference
The symbol is the Greek letter pi. It stands for a number
that can never be found exactly. It is approximately
3.14
Evaluate the CIRCUMFERENCE
Always, write the formula (rule)
Diameter = ?cm
C = d
d = C ÷
d = C ÷ 3.14
d = 40 ÷ 3.14
d = 12.73
How to calculate the diameter from the circumference
If the circumference is 40 cm. evaluate the DIAMETER
Always, write the formula (rule)
Diameter Radius Circumference
1 24
2 14
3 17
4 30
5 22
6 120
7 78
8 88
9 120
10 340
Rememberd = 2 X rr = d ÷ 2
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
Calculate an Arc Length
Level 7
720
A
B
How to Calculate an Arc Length
Calculate the arc length AB for a circle with a diameter of 12 cm.
CircumferenceC = 3.14 x 12C = 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
x0
A
B
The FORMULA for an Arc Length
Calculate the arc length AB for a circle with a
diameter of d
AB = x/360( d)
AB = (x ÷ 360) x 3.14 x d
Divide the arc length’s angle by 360 then multiply this by the circumference
x0
A
B
Using the FORMULA for an Arc
Calculate the arc length AB for these circles
AB = x/360( d)
AB = (x ÷ 360) x 3.14 x d
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
x0
A
B
Using the FORMULA for an Arc
Calculate the arc length AB for these circles
AB = x/360( d)
AB = (x ÷ 360) x 3.14 x d
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
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
1.57
When a wheel makes one complete
revolution, the distance that it travels
is its circumferenc
e
How many times will a wheel with a diameter of 0.5 metre rotate when it travels distance of 100 metres?
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
100 metres
Wheel’s 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
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 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
A car’s wheels have a diameter of 45 cm. How many times will the wheel revolve during a journey of 100 km?Level 8
A bike’s wheels have a diameter of 70 cm. How many times will the wheel revolve during a journey of 50 km?
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