Circumference

Calculate the Circumference Using the Correct Formula

18 Apr 2023

Calculate the circumference and area of a circle and the

area of an annulus

Calculate the circumference and area of a circle and the

area of an annulus

Level 6© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

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Diameter = 12 cm

C = Πd

C = 3.14 X 12

C = 37.68 cm

How to calculate the circumference

© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

The rule to find the circumference is Π x diameter.

The value of Π is approximately 3.14

The rule to find the circumference is Π x diameter.


To distance all the way around a

circle is called the

circumference.

To distance all the way around a

circle is called the

circumference.

Write down the rule.


Write down what

the rule actually means

Write down what



Diameter = ?cm

d = C ÷ Π

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



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© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk


The CircleRADIUS The distance from the centre to the edge

DIAMETER The distance from one side to the other passing through the centre

Π = 3.14 (approximately)D = 2 x R and R = D ÷ 2



Radius = 5 cm

Area = Πr2

A = 3.14 x 5 x 5

A = 78.5 cm2

How to calculate the area of a circle


The rule to find the area is A = Π x r2.


The rule to find the area is A = Π x r2.




Write down what


Write down what



4 cm3 cm

6 cm

A = Πr2

A = 3.14 x 4 x 4

A = 50.24 cm2

A = Πr2

A = 3.14 x 3 x 3

A = 28.26 cm2

A = Πr2

A = 3.14 x 6 x 6

A = 113.04 cm2

10 cm

8 cm 12 cm

314 cm2

200.96 cm2

452.16 cm2

1.

2. 3.

4. 5. 6.



Calculate the areas of the following circles1 Radius = 10 cm 5 Diameter = 24

cm2 Radius = 15 cm 6 Diameter = 21

cm3 Radius = 13.5

cm7 Diameter = 3.8

cm4 Radius = 8.75

cm8 Diameter = 12.5

cm© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk


Calculate the areas of the following circles1 314 cm2 5 452.16 cm2

2 706.5 cm2 6 346.19 cm2 (2 dp)

3 572.265 cm2 7 11.34 cm2 (2 dp)4 240.41 cm2 (2

dp)8 122.66 cm2 (2

dp)



If you know the area and need to calculate the radius the formula is:

r = √(A ÷ π)

For example, what is the radius of a circle with an area of 120 cm2?

r = √( 120 ÷ 3.14)

r = √38.217

r = 6.18 cm to 2 d.p.


Calculate the radii of circles with the following areas.

1 314 cm2 5 452.16 cm2

2 706.5 cm2 6 346.19 cm2

3 572.265 cm2 7 11.34 cm2

4 240.41 cm2 8 122.66 cm2


The radii for the previous question

1 Radius = 10 cm 5 Radius = 12 cm

2 Radius = 15 cm 6 Radius = 10.5 cm

3 Radius = 13.5 cm

7 Radius = 1.9 cm

4 Radius = 8.75 cm

8 Radius = 6.25 cm


The area of an ANNULUS

R

r

For this example R = 10 metres and r = 5 metres

A = π(R + r)(R – r)

A = π(15 +5)(15 – 5)

A = 3.14 x 15 x 5

A = 235.5 metres2


r R1. 4 62. 3 73. 5 154. 12 185. 4 166. 13 197. 6.5 13.5

Calculate the area of each annulus described in the table.


r R units2

1. 4 6 62.82. 3 7 125.63. 5 15 6284. 12 18 565.25. 4 16 753.66. 13 19 602.887. 6.5 13.5 439.6


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Circumference