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?