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11.5 Area of Circles and Sectors

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11.5 Area of Circles and
Sectors
Theorem
The equation for the Area of a Circle
Area equals radius squared times pi.
Ar 
2
9
Theorem
The equation for the Area of a Circle
Area equals radius squared times pi.
Ar 
A  9 
2
2
9
A  81
Definition of a Circle Sector
A circle sector is a fraction of the circle
enclosed by two radii and an arc.
Minor Sector
Major Sector
Pac  Man
Theorem
The Equation for the Area of a Sector
Sector 

360
r  
2
135 
11
Theorem
The Equation for the Area of a Sector
Sector 

360
r  
2
135 2
11  
Sector 
360
3
Sector  121 
8
 45.375
135 
11
Find the Radius
The Sector Area is 15 Central Angle 150
Sector 
150 

360
r  
150 2
r 
15 
360
2
Find the Radius
The Sector Area is 15 Central Angle 150
Sector 
150 

360
r  
150 2
r 
15 
360
15 
5 2
r
12
2
Find the Radius
The Sector Area is 15 Central Angle 150
Sector 
150 

r  
2
360
150 2
r 
15 
360
5
15  r 2
12
r2
 12 
 15   36
5
r 2  36  r 2   36
Find the Radius
The Sector Area is 15 Central Angle 150
Sector 
150 
15 
15 

360
r  
150 2
r 
360
5 2
r
12
2
 12 
r 2  15   36
5
r 2  36  r 2   36
r 6
Find the Shaded Area
Hint : find the Area of the Circle – the Area of the triangle
60
4
4
60
60
4
Find the Shaded Area
Hint : find the Area of the Circle – the Area of the triangle
60
4
60
4
2
2
4
60
2

3
2x
x
30
2 x 3
2
2x  2 
3
2x  r 
4
3
Find the Shaded Area
Hint : find the Area of the Circle – the Area of the triangle
16
 4 
Area of the circle  
  
3
 3
60
4
60
4
2
2
4
60
Area of triagnle 
1 2
A  4  3  4 3
4
1
2
 3  side
4
Find the Shaded Area
Hint : find the Area of the Circle – the Area of the triangle
16
 4 
Area of the circle  
  
3
 3
60
4
60
4
2
2
4
60
Area of triagnle 
1
2
 3  side
4
1 2
A  4  3  4 3
4
16
RED area    4 3
3
Homework
Page 695-698
# 10 – 28 even,
31 – 37, 40, 41,
43 - 44
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