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www.mathsrevision.c om MNU 3-11a MTH 3-11a The Circle The Circle Diameter = Circumference ÷ π Investigation of the Circle Composite shapes Perimeter

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### Transcript of Www.mathsrevision.com MNU 3-11a MTH 3-11a The Circle Diameter = Circumference ÷ π Investigation of...

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MNU 3-11aMTH 3-11a

The CircleThe Circle

Diameter = Circumference

÷ π

Investigation of the Circle

Composite shapes Perimeter

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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 22

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.

diameter

The diameter is measured from one edge to the other

passing through the centre of the circle.

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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 33

Circle Circle InvestigationInvestigation

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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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 44

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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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 55

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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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 66

Measuring the Circumference Measuring the Circumference

of a circleof a circle

Flexible tape measure

Take a tape measure and put it round the circle

O

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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 77

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 point

End point

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MNU 3-11aMTH 3-11a

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

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

Circle I nvestigation Calculations

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

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

Circle I nvestigation Calculations

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

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

Circle I nvestigation Calculations

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

1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4 12.6 4.0

5

6

7

8

Circle I nvestigation Calculations

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

1 17.6 5.5

2 15.9 5.0

3 14.3 4.5

4

5

6

7

8

Circle I nvestigation Calculations

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

1 17.6 5.5

2 15.9 5.0

3

4

5

6

7

8

Circle I nvestigation Calculations

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

1 17.6 5.5

2

3

4

5

6

7

8

Circle I nvestigation Calculations

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

1

2

3

4

5

6

7

8

Circle I nvestigation Calculations

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

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

Circle I nvestigation Calculations

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 88

Circle InvestigationCircle Investigation

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

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

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Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 99

Circle InvestigationCircle Investigation

C D C circumference

D diameter

3.14

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 π

Pronounced “Pi”

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try TJ3a

Ex 1 Q2Ch10 (page 88)

The CircleThe Circle

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Starter QuestionsStarter Questions

2. Calculate (-3m) x (-4m)

1. Name this shape.

3. Find the mean, median and mode of

data set 3,5,5,7,10

4

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Recall knowledge of circles Recall knowledge of circles so far.so far.

1. We are learning to calculate the perimeter of composite shapes that including parts of a circle.

PerimeterPerimeter

2.2. Solve mixed problems by Solve mixed problems by applying all our knowledge applying all our knowledge so far.so far.

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Main Parts of a Circle

Main parts of the circle

O

Circumference2D r

12

r D

C D

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Calculating the Calculating the CircumferenceCircumference

10cm

2cm

C D2D r 4D cm

Example : Find the length of the circumference (Perimeter)

of each circle

C D 10

31.4 cm 4

12.56 cm

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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 1515

Example Calculate the curved part of this shape.Solution

C D

1curved length 12

4

length 9.4curved m

6m 1curved length

4D

90o

curved length 3

Calculating the Calculating the CircumferenceCircumference

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Example Find the perimeter for the semi-circle shape ?

Solution

120

2P D

1

P 20 202

180o

P 10 20

P 51.4cm

Composite Composite PerimeterPerimeter

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MNU 3-11aMTH 3-11a

Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 1717

Example Find the perimeter of the shape below ?Solution

18 8

4P D

116 8 8

4P

28.6P cm

8cm

90o

4 16P

Composite Composite PerimeterPerimeter

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Example : Find the perimeter of this shape

20cm

5 cm

Perimeter = 3 sides + semicircle

15 20 5 20

2 P

30 10 P

61 4.P cm

Composite Composite PerimeterPerimeter

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try TJ3a

Ex 2Ch10 (page 91)

The CircleThe Circle

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Starter Starter QuestionsQuestions

2. Calculate (5d) x (-6d)

1. Name the shape.

3. Find the mean, median and mode of

data set 3,5,6,7,9

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1. We are learning to find the diameter of a circle if we know the circumference.

Finding the DiameterFinding the Diameter

The Circle

2.2. Solve diameter problems.Solve diameter problems.

1.1. Understand how to Understand how to rearrange circumference rearrange circumference formula to find diameter.formula to find diameter.

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

We can easily rearrange the circumference formula so that we have the diameter D on one side.

Finding the DiameterFinding the Diameter The Circle

You have 1 minute to rearrange equation.

C D

CD

Remember

change side change sign

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

C = 62.8 cm

C

D

Examples : Find the diameter of each circle given the circumference.

62.8

20 cm5 cm

20cm

C =15.7 cm

C

D

15.7

5cm

Finding the DiameterFinding the Diameter

The Circle

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MNU 3-11aMTH 3-11a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try TJ3a

Ex 3Ch10 (page 93)

The CircleThe CircleHave you updated