Www.mathsrevision.com Level 2 Wednesday, 19 August 2015Wednesday, 19 August 2015Wednesday, 19 August...

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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 11

The CircleThe Circle

Main Parts of a Circle

Formula for Circumference


Starter Questions Starter Questions

1. What shape has an infinte line symmetry.

2. Solve 3x+7 28.

3. Find the perimeter of the star.

4. Convert your answer to Q3 to (m).

7cm

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Main part of a CircleMain part of a Circle

Learning IntentionLearning Intention

We are learning to identify the main parts of a circle.o identify the main parts of a circle.

Success CriteriaSuccess Criteria

1.1. Understand the terms Understand the terms circumference, diameter and radius.circumference, diameter and radius.

2. 2. Identify them on a circle.Identify them on a circle.

3. 3. Calculate the circumference using formula.Calculate the circumference using formula.

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Main parts of the circle

Main part of a CircleMain part of a Circle

radius

O

Circumference Diameter2D r

12

r D

C D

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Main part of a Main part of a CircleCircle

10cm

2cm

12

r D 5r cm

2D r 4D cm

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Main part of a Main part of a CircleCircle

Your turn Exercise 1 Your turn Exercise 1 Chapter 19Chapter 19Page 228Page 228


Starter QuestionsStarter Questions

1. The diameter of a circle is 10cm. What is the radius.

2. The radius of a circle is 3.5cm. What is the diameter.

3. Find the perimeter of the star.

4. Convert your answer to Q3 to (mm).

5cm

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Stars In Your EyesStars In Your Eyes

“Today Matthew we are going to be”

Archimedes of Syracuse

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The Greek mathematician Archimedes of Syracuse (287- 212 BC) who flourished in Sicily is generally considered to be the greatest

mathematician of ancient times. He is credited with determining the relationship between the diameter and the circumference of a circle.

This was first recorded by Archimedes in the book Measurement of a Circle (225 BC).

In this investigation we are going to attempt to follow Archimedes stepsand arrive at the equation for determining the circumference for

any given circle.

History of CirclesHistory of Circles75 years old

22931 years old

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Parts of the CircleParts of the Circle

Circumference

O

O = centre of circle

The radius is measured fromthe centre of the circle

to the edge.

radius

diameter

The diameter is measured from one edge to the other

passing through the centre of the circle.

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Circle InvestigationCircle Investigation

Construct a table shown below to enable usto record our results.

Circle Circumference = C Diameter = D C+D= C- D= C/D= CxD=

1

2

3

4

5

6

7

8

Circle I nvestigation Calculations

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Investigation of the CircleInvestigation of the Circle

To find a relationship between

the diameter and circumference of a given circle.

How can we measure the diameter and circumference

O

Our Investigation

Question ?

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Measuring the Diameter Measuring the Diameter

of a circleof a circle

The diameter is the largest distance between one side of a circle to the other

passing through the centre O.

O

O Use a ruler

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Measuring the Circumference Measuring the Circumference

of a circleof a circle

Flexible tape measure

Take a tape measure and put it round the circle

Read off the measurement

O

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Measuring the Circumference of a Measuring the Circumference of a circlecircle

Roll along an even surface

One complete rotation equals the length of the circumference

Be careful to avoid slip!

Starting pointEnd point

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1 17.6 5.5 23.1 12.1 3.2 96.8

2 15.9 5.0 20.9 10.9 3.2 79.5

3 14.3 4.5 18.8 9.8 3.2 64.4

4 12.6 4.0 16.6 8.6 3.2 50.4

5 11.2 3.5 14.7 7.7 3.2 39.2

6 9.5 3.0 12.5 6.5 3.2 28.5

7 8.0 2.5 10.5 5.5 3.2 20.0

8 6.4 2.0 8.4 4.4 3.2 12.8

CalculationsCircle I nvestigation


1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4 12.6 4.0

5 11.2 3.5

6 9.5 3.0

7 8.0 2.5

8



1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4 12.6 4.0

5 11.2 3.5

6 9.5 3.0

7

8



1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4 12.6 4.0

5 11.2 3.5

6

7

8



1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4 12.6 4.0

5

6

7

8



1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4

5

6

7

8



1 17.6 5.5

2 15.9 5.0

3

4

5

6

7

8



1 17.6 5.5

2

3

4

5

6

7

8



1

2

3

4

5

6

7

8



1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4 12.6 4.0

5 11.2 3.5

6 9.5 3.0

7 8.0 2.5

8 6.4 2.0


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C D C circumference

D diameter

Using your results write down, in your own words, an approximate relationship between the circumference and diameter for a given circle.

“Circumference approximately equals three and bit diameters”Actual value is 3.14 which we write as

3.14

Pronounced “Pi”

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Chapter 19 Exercise 2 Page 229 Q2

Circle InvestigationCircle Investigationw

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