The Circle 2 [PPS]

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Transcript The Circle 2 [PPS]

The Circle
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Level 3
Circumference of the circle
Diameter
=
Circumference ÷
Area of a circle
Fractions of a circle
21-Jul-15
Created by Mr. Lafferty Maths Dept.
π
Starter Questions
Level 3
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1. A house appreciates by 20% in one year.
If its initial price was £60 000. How much is it now.
2. Simplify the ratio 34 : 72
3.
Tidy up the expression
15e + 3d +14d + 10e
5.
3cm
Find the area of the shape.
21-Jul-15
Created by Mr. Lafferty Maths Dept.
6cm
Main Parts of a Circle
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Level 3
Revision of 2
Learning Intention
Success Criteria
1. To revise the basics of the
circle.
21-Jul-15
1.
Remember the terms
circumference,
diameter and radius.
2.
Identify them on a
circle.
3.
Calculate the
circumference using
formula.
Created by Mr. Lafferty Maths Dept.
Main Parts of a Circle
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Level 3
Revision of 2
Main parts of the circle
radius
1
r  D
2
O
Diameter
Circumference
D  2r
C  D
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Main part of a Circle
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Level 3
Revision of 2
Example : Find the length of the circumference (Perimeter) of each
circle
C   D    10
 31.4cm
21-Jul-15
D  2r
D  4cm
C  D    4
 12.56cm
Created by Mr. Lafferty Maths Dept.
Main part of a Circle
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Level 3
Revision of 2
Now try Exercise 1
Ch29 (page 118)
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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Level 3
1.
Find the area of the shape.
8
5
4
2. Calculate (-3m) x (-4m)
3.
Find the mean, median and mode of
data set
21-Jul-15
3,5,5,7,10
Created by Mr. Lafferty Maths Dept.
Finding the Diameter
The Circle
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Level 3
Learning Intention
Success Criteria
1. We are learning we can find
diameter of a circle if we
know the circumference.
1. Understand how to
rearrange circumference
formula to find diameter.
2. Solve diameter problems.
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Finding the Diameter
The Circle
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Level 3
We can easily rearrange the circumference formula
so that we have the diameter D on one side.
C  D
D
21-Jul-15
C

Created by Mr. Lafferty Maths Dept.
You have 1
minute to
rearrange
equation.
Remember
change side
change sign
Finding the Diameter
The Circle
Level 3
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Example : Find the diameter of each circle given the circumference.
C = 62.8 cm
21-Jul-15
C =15.7 cm
C 62.8
D



 20 cm
C 15.7
D



 5 cm
Created by Mr. Lafferty Maths Dept.
Finding the Diameter
The Circle
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Level 3
Now try Exercise 2
Ch29 (page 121)
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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Level 3
1.
Find the area of the shape.
6
5
2. Calculate (5b) x (-4b)
3.
Find the mean, median and mode of
data set
21-Jul-15
4,8,7,7,8,10
Created by Mr. Lafferty Maths Dept.
Area of a Circle
Peeling an
Levelorange
3
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A
x
circumference
r
O
A
x
2 r
B
O
circumference (2 r )
What do we call the distance OA in terms of
the large circle.
radius (r )
What do we call the distance AB in terms of
the large circle.
Area of a Circle
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Level 3
21-Jul-15
A
r
O
2 r
x
B
What is the formula for the area
of a right-angle triangle.
1
A   base  height
2
Use this formula to work out
the area for a circle.
1
A   r  2 r
2
A   r2
Created by Mr. Lafferty Maths Dept.
Area of a Circle
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Level 3
8
If we break the circle
into equal sectors
And lay them out side by side
We get very close
to a rectangle.
1
7
2
6
3
5
4
1
2
3
4
5
6
7
8
Demo
Tuesday, 21 July 2015
Created by Mr Lafferty
15
Area of a Circle
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Level 3
1
2
3
4
5
6
7
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
thinner and thinner
sectors
r
r
Tuesday, 21 July 2015
Created by Mr Lafferty
16
Area of a Circle
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Level 3
r
r
Area of a rectangle  l  b
Area of a rectangle   r  r   r 2
But the area inside this rectangle is also the area of the circle
Area = πr2
Tuesday, 21 July 2015
Created by Mr Lafferty
17
Area of a circle
Level 3
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Q.
Find the area of the circle ?
Solution
4cm
A  r
2
A  4
2
A  50.26cm 2
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Area of a circle
Level 3
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Q.
The diameter of the circle is 60cm.
Find area of the circle?
Solution
A  r
2
D
60
r  
 30cm
2
2
A    30
2
A  2826 cm
21-Jul-15
Created by Mr. Lafferty Maths Dept.
2
Area of a Circle
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Level 3
What have we learned so far
Circumference   D
Area   r
21-Jul-15
2
Created by Mr. Lafferty Maths Dept.
Area of a Circle
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Level 3
Now try Exercise 3
Ch29 (page 123)
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
Level 3
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1.
Find the area of the shape.
4
2. Calculate (-7) x (-12)  6
3.
Find the mean, median and mode of
data set
21-Jul-15
6,7,3,10,8,10,12
Created by Mr. Lafferty Maths Dept.
Mixed Problems
The Circle
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Level 3
Learning Intention
Success Criteria
1. We are learning to solve
problems by applying our
knowledge of circles.
21-Jul-15
1. Recall knowledge of circles
so far.
2. Solve mixed problems by
applying all our knowledge so
far.
Created by Mr. Lafferty Maths Dept.
Mixed Problems
The Circle
www.mathsrevision.com
Level 3
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 !
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Mixed Problems
The Circle
Level 3
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Example 1 : Find the area of the shape
Area = rectangle + semicircle
1 2
A  l b 
r
2
5 cm
20cm
21-Jul-15
1
2
A  20  5 
 (10)
2
A  100  157
A  257 cm2
Created by Mr. Lafferty Maths Dept.
Mixed Problems
The Circle
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Level 3
Example 2 : A circle is contained in a square.
Find the grey shaded area below.
8cm
Area = square - circle
Al
2
- r
2
A  8  8 -  (4)2
A  64 - 50.24
A  13.76 cm 2
21-Jul-15
Created by Mr. Lafferty Maths Dept.
Mixed Problems
The Circle
www.mathsrevision.com
Level 3
Now try Exercise 4
Ch29 (page 125)
21-Jul-15
Created by Mr. Lafferty Maths Dept.