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The Circle. Circumference of the circle. Diameter = Circumference ÷ π. www.mathsrevision.com. Area of a circle. Fractions of a circle. Starter Questions. www.mathsrevision.com. Main Parts of a Circle. Revision of Level E. Learning Intention. Success Criteria.

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Presentation Transcript
the circle

The Circle

Circumference of the circle

Diameter = Circumference ÷π

www.mathsrevision.com

Area of a circle

Fractions of a circle

Created by Mr. Lafferty Maths Dept.

starter questions

Starter Questions

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

slide3

Main Parts of a Circle

Revision of Level E

Learning Intention

Success Criteria

  • To revise the basics of the circle.
  • 1. Know the terms circumference, diameter and radius.
  • 2. Identify them on a circle.
  • 3. Calculate the circumference using formula.

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

slide4

radius

Diameter

Circumference

Main Parts of a Circle

Revision

Main parts of the circle

O

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Created by Mr. Lafferty Maths Dept.

slide5

Main part of a Circle

Revision

Example : Find the length of the circumference (Perimeter) of each

circle

2cm

10cm

Created by Mr. Lafferty Maths Dept.

slide6

Main part of a Circle

Revision

Now try Ex 1

Ch10 (page 112)

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Created by Mr. Lafferty Maths Dept.

starter questions1

Starter Questions

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Created by Mr. Lafferty Maths Dept.

slide8

Finding the Diameter

The Circle

Learning Intention

Success Criteria

  • Understand how to rearrange circumference formula to find diameter.
  • 1. To explain how we can find diameter of a circle if we know the circumference.
  • 2. Solve diameter problems.

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Created by Mr. Lafferty Maths Dept.

slide9

Finding the Diameter

The Circle

We can easily rearrange the circumference formula

so that we have the diameter D on one side.

You have 1 minute to rearrange equation.

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Remember change side change sign

Created by Mr. Lafferty Maths Dept.

slide10

Finding the Diameter

The Circle

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

C = 62.8 cm

C =15.7 cm

5cm

20cm

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Created by Mr. Lafferty Maths Dept.

slide11

Finding the Diameter

The Circle

Now try Ex 2

Ch10 (page 114)

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Created by Mr. Lafferty Maths Dept.

starter questions2

Starter Questions

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Created by Mr. Lafferty Maths Dept.

area of a circle

Peeling an

orange

Area of a Circle

A

circumference

A

B

x

x

O

O

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  • What do we call the distance OA in terms of
  • the large circle.
  • What do we call the distance AB in terms of the large circle.
slide14

A

B

x

O

Area of a Circle

  • What is the formula for the area
  • of a right-angle triangle.
  • Use this formula to work out
  • the area for a circle.

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Created by Mr. Lafferty Maths Dept.

slide15

If we break the circle

into equal sectors

And lay them out side by side

We get very close

to a rectangle.

1

8

2

2

7

1

3

6

5

8

6

4

4

3

7

5

Area of a Circle

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Created by Mr Lafferty

slide16

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.

8

6

4

2

3

7

1

5

thinner and thinner

sectors

Area of a Circle

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Created by Mr Lafferty

slide17

Area of a Circle

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

Created by Mr Lafferty

area of a circle1

Area of a circle

Solution

Q.Find the area of the circle ?

4cm

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Created by Mr. Lafferty Maths Dept.

area of a circle2

Area of a circle

Solution

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

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Created by Mr. Lafferty Maths Dept.

slide20

Area of a Circle

What have we learned so far

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slide21

Area of a Circle

Now try Ex 3

Ch10 (page 116)

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Created by Mr. Lafferty Maths Dept.

starter questions3

Starter Questions

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Created by Mr. Lafferty Maths Dept.

slide23

Mixed Problems

The Circle

Learning Intention

Success Criteria

  • Recall knowledge of circles so far.
  • 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far.
  • 2. Solve mixed problems by applying all our knowledge so far.

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Created by Mr. Lafferty Maths Dept.

slide24

Mixed 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 !

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

Created by Mr. Lafferty Maths Dept.

slide25

5 cm

20cm

Mixed Problems

The Circle

Example 1 : Find the area of the shape

Area = rectangle + semicircle

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Created by Mr. Lafferty Maths Dept.

slide26

Mixed Problems

The Circle

Example 2 : A circle is contained in a square.

Find the grey shaded area below.

Area = square - circle

8cm

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Created by Mr. Lafferty Maths Dept.

slide27

Mixed Problems

The Circle

Now try Ex 4

Ch10 (page 119)

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Created by Mr. Lafferty Maths Dept.

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