Www.mathsrevision.com MNU 311a MTH 311a The Circle Diameter = Circumference ÷ π Investigation of...

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Transcript of Www.mathsrevision.com MNU 311a MTH 311a The Circle Diameter = Circumference ÷ π Investigation of...
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MNU 311aMTH 311a
The CircleThe Circle
Diameter = Circumference
÷ π
Investigation of the Circle
Composite shapes Perimeter
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MNU 311aMTH 311a
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.
radius
diameter
The diameter is measured from one edge to the other
passing through the centre of the circle.
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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 311aMTH 311a
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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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 311aMTH 311a
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
Read off the measurement
O
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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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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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MNU 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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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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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Friday 21 April 2023Friday 21 April 2023 Created by Mr Lafferty Created by Mr Lafferty 1616
Example Find the perimeter for the semicircle shape ?
Solution
120
2P D
1
P 20 202
180o
P 10 20
P 51.4cm
Composite Composite PerimeterPerimeter
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MNU 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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 311aMTH 311a
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
your Learning Log ?