1. The Circle Levels 5  8 Know the names of a circle’s features
Friday, 21 April 2017
Know the names of a circle’s 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. Where can you see i) a segment ii) a sector iii) an 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
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 circle’s 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 8 24 6 36 10 20 60 5 30 15 90 3 18 7 14 42

9. 30 cm 6 cm 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. C = d C = 3.14 X 12 C = 37.68 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 8 889 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
376.8
156 78
489.84 8
176 88
552.64 9
38.22
19.11 10
108.28
54.14
340

15. Calculate an Arc Length
Level 7

16. A 720 B Circumference C = 3.14 x 12 C = 37.6 cm
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

17. 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 length’s angle by 360 then multiply this by the circumference

18. x0 A B AB = x/360( d) AB = (x ÷ 360) x 3.14 x d
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 1.
144 12 4.
270 60 2. 48 40 5. 24 36 3.
180 25 6. 70

19. x0 A B AB = x/360( d) AB = (x ÷ 360) x 3.14 x d
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 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
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
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. Wheel’s Diameter Circumference Distance of Journey
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

24. 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

25. A bike’s wheels have a diameter of 70 cm
A bike’s wheels have a diameter of 70 cm. How many times will the wheel revolve during a journey of 50 km?
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