1. This document discusses calculating properties of circles such as circumference, diameter, radius, arc length, and number of revolutions of a wheel on a journey. 2. It provides formulas for calculating circumference (C=πd), diameter (d=C/π), and arc length (Arc Length= (Angle/360) x Circumference) and examples of using these formulas. 3. It also explains how to calculate the number of revolutions a wheel makes by dividing the journey distance by the circumference.

1. The Circle Monday 4 June 2012
1. Know the names of a circle’s features
2. Calculate the circumference
3. Calculate an arc length
4. Deal with the revolution of wheels and
journey problem
Why am
Levels 5  8 I doing
A wheel is a circle! this?
Circles in design – Mickey OK -
Mouse is made from circles What
A real favourite SAT and
have I got
GCSE question 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
Segment other passing through the centre
Sector DIAMETER
The distance all of the way round
the edge CIRCUMFERENCE
An ARC is the name The blue line CHORD
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
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? 30 cm
• A circle has a
circumference of 18 cm.
Approximately, what is its
diameter? 6 cm

10. Calculate the
Circumference
Using the Correct
Formula
Level 6

11. How to calculate the circumference
Evaluate the Always, write
CIRCUMFERENCE
C= d the formula
(rule)
Diameter = 12 cm 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

12. How to calculate the diameter from the
circumference
Always, write
If the
circumference is 40 C= d the formula
(rule)
cm. evaluate the
DIAMETER
d=C÷
Diameter = ?cm
d = C ÷ 3.14
d = 40 ÷ 3.14
d = 12.73

13. Diameter Radius Circumference
1 24
2 14
3 17
4 30
5 22
6 120 Remember
d=2Xr
7 78 r=d÷2
8 88
9 120
10 340

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 Calculate the arc length
Length A AB for a circle with a
diameter of 12 cm.
720 Circumference
B C = 3.14 x 12
C = 37.6 cm
But we only want the arc length
AB. This is 720 of the circle and AB = 0.2 x C
because there are 3600 in a AB = 0.2 x 37.6
circle, this is 72 ÷ 360 = 0.2 as AB = 5.52
a decimal fraction of the
circumference

17. The FORMULA for an Calculate the arc length
Arc Length A AB for a circle with a
diameter of d
x 0
AB = x/360( d)
B
AB = (x ÷ 360) x 3.14 x d
Divide the arc length’s angle
by 360 then multiply this by
the circumference

18. Using the FORMULA for Calculate the arc length
an Arc A AB for these circles
AB = x/360( d)
x0
B 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

19. Using the FORMULA for Calculate the arc length
an Arc A AB for these circles
AB = x/360( d)
x0
B 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

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
1.57 1. Find the
circumference of the
When a wheel wheel
makes one
complete C = 3.14 x 0.5
revolution, the C = 1.57
distance that
it travels is its 2. Divide this into 100 to
circumference find the number of
revolutions
Revs = 100 ÷ 1.57
Revs = 63.7 times

23. 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

24. 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

25. 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
Level 8 km?