Chapter 7 Lesson 7

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Chapter 7 Lesson 7

• Objective To find the areas of circles, sectors,
  and segments of circles.

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Theorem 7-15 Area of a Circle The area of a
circle if the product of and the square of the
radius.
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Example 1Area of a Circle
How much more pizza is in a 12-in. diameter pizza
than in a 10-in. pizza?
Small Pizza
Medium Pizza
Find the radius.
Find the radius.
Find the area.
Find the area.
Find the difference in the areas.
                                                
                                                  
                                               
                                                  
                                                  
   There is about 35 in.2 more pizza in the
medium pizza.
plug into your calculator
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Sector of a circle Is a region bounded by an arc
of the circle and the two radii to the arcs
endpoints.
Theorem 7-16  Area of a Sector of a Circle
The area of a sector of a
circle is the product of the ratio and the
area of the circle. Area of sector AOB     
pr2
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Example 2Finding the Area of a Sector of a
Circle
Find the area of sector ZOM. Leave your answer in
terms of p.                                    
                                            
                              
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Example 3Finding the Area of a Sector of a
Circle
Find the area of sector ACB. Leave your answer in
terms of p.                                    
                                            
                              
B
6 m
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Segment of a Circle
A part of a circle bounded by an arc and the
segment joining its endpoints. To find the area
of a segment for a minor arc, draw radii to form
a sector. The area of the segment equals the area
of the sector minus the area of the triangle
formed.                                        
                                                  
                                                  
                                            
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Example 4Finding the Area of a Segment of a
Circle
Find the area of the shaded segment. Round your
answer to the nearest tenth.
                                                  
                                                  
                                                  
                                                  
                         
Find the area of sector AOB.
Find the area of the segment.
Find the area of ? AOB.
The area of the segment is about 28.5 in.2
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Example 5Finding the Area of a Segment of a
Circle
A circle has a radius of 24 ft. Find the are of
the smaller segment of the circle determined by a
120 arc. Round your answer to the nearest
tenth.                                          
                                                  
                                                  
                                                  
                                  
Find the area of the sector.
24
24
120
60
hyp. 2SL 242SL 12SL
LLv3SL LLv312 LL12v3
Find the area of ? AOB.
Find the area of the segment.
The area of the segment is about 353.5 ft.2
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Assignment
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