Level 3 14-Aug-15Created by Mr. Lafferty Maths Dept. The Circle Circumference of the circle Diameter = Circumference ÷ π Area of

Level 3

19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

The CircleThe Circle

Circumference of the circle

Diameter = Circumference

÷ π

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Area of a circle

Fractions of a circle

Level 3


Starter QuestionsStarter Questionsw

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2. Simplif y the ratio 34:72

1. A house appreciates by 20% in one year.

I f its initial price was £60 000. How much is it now.

3. Tidy up the expression

15e + 3d +14d + 10e

5. Find the area of the shape.

6cm

3cm

Level 3

19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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1. To revise the basics of the circle.

Main Parts of a Circle

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

2.2. Identify them on a Identify them on a circle.circle.

3.3. Calculate the Calculate the circumference using circumference using formula.formula.

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Main Parts of a Circle

Main parts of the circle

O

Diameter2D r

12

r D

C D

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Main part of a Main part of a CircleCircle

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

Revision of 2

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Now try Exercise 1Ch29 (page 118)

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Main part of a CircleMain part of a Circle

Level 3



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


3. Find the mean, median and mode of

data set 3,5,5,7,10

4

5

8

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1. We are learning we can find 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.

Level 3


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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

Level 3


C = 62.8 cm

C

D

Example : 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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Finding the DiameterFinding the Diameter The Circle

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2. Calculate (5b) x (-4b)



data set 4,8,7,7,8,10

6

5

Level 3

What do we call the distance AB in terms of the large circle.

Area of a CircleArea of a Circle

(2 )circumference r

( )radius r

O

A x

O

Ax B

What do we call the distance OA in terms ofthe large circle.

circumference

Peeling anorange

2 r

r

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r

2 r

1

2A base height

2A r19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

What is the formula for the area of a right-angle triangle.

O

Ax

B

Use this formula to work outthe area for a circle.

12

2A r r

Area of a CircleArea of a Circlew

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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 1515

23

4

1

2

3

456

7

8

1 56

78

If we break the circleinto equal sectors

And lay them out side by side We get very close

to a rectangle.

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mArea of a CircleArea of a Circle

Demo

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12

34

56

78

thinner and thinnersectors

If we cut the sectors Thinner and thinner then we get closer and closer

to a rectangle. Hence we can represent the area of a circle

by a rectangle.

r

r

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r

r

Area of a rectangle l b 2Area of a rectangle r r r

But the area inside this rectangle is also the area of the circle

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Area = πr2

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Area of a circleArea of a circle

Q. Find the area of the circle ?

SolutionSolution

2A r

24A250.26A cm

4cm

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Area of a circleArea of a circle

Q. The diameter of the circle is 60cm. Find area of the circle?

SolutionSolution

2A r60

302 2

D

r cm

230A22826 A cm

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What have we learned so far

Circumference D

2Area r

Area of a CircleArea of a Circlew

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Area of a CircleArea of a Circle

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2. Calculate (-7) x (-12) 6



data set 6,7,3,10,8,10,12

4

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

1. We are learning to solve problems by applying our knowledge of circles.

Mixed ProblemsMixed Problems

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

The Circle

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Mixed ProblemsMixed Problems The Circle

Things to think about when doing exercise.

The area of a semicircle ……. Find whole circle then half it !

The area of a quarter circle …….Find whole circle then quarter it !

Composite area …….Find each area and add them together !

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Example 1 : Find the area of the shape

20cm

5 cm

Area = rectangle + semicircle

21

2A l b r

2120 5 10

2( )A

100 157 A 2257 cmA

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Example 2 : A circle is contained in a square.Find the grey shaded area below.

Area = square - circle

2 2 -A l r28 8 4- ( )A

64 - 50.24A 213 76 cm.A

8cm

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Documents

Level 3 14-Aug-15Created by Mr. Lafferty Maths Dept. The Circle Circumference of the circle Diameter = Circumference ÷ π Area of