Chapter 7 Chapter 7 Lesson 7Lesson 7

Objective:Objective: To find To find the areas of circles, the areas of circles,

sectors, and sectors, and segments of circles.segments of circles.

Theorem 7-15:Theorem 7-15: Area of a CircleArea of a Circle

The area of a circle is the product of and the square of the radius.

2rA

rrOO

Example 1:Example 1:Area of a CircleArea of a Circle

How much more pizza is in a 12-in. diameter pizza How much more pizza is in a 12-in. diameter pizza than in a 10-in. pizza?than in a 10-in. pizza?

Small PizzaSmall Pizza Medium PizzaMedium Pizza

Find the radius.Find the radius. Find the radius.Find the radius.

Find the area.Find the area. Find the area.Find the area.

Find the difference in the areas.Find the difference in the areas.

                                                                                                                                                                                                                                                        There is about 35 in.2 more pizza in the medium pizza.

plug into your plug into your calculatorcalculator

Sector of a circle

Is a region bounded by an arc of the circle and the two radii to the arc’s endpoints.

Theorem 7-16:Theorem 7-16:    Area of a Sector of a CircleArea of a Sector of a Circle The area of a sector of a circle is the product of The area of a sector of a circle is the product of

the ratio and the area of the circle. the ratio and the area of the circle. Area of sector Area of sector AOBAOB =     • =     • πrπr22

Example 2:Example 2:Finding the Area of a Sector of a

Circle

Find the area of sector ZOM. Leave your answer in terms of π.

                                       

                                                                     

Find the area of sector ACB. Leave your answer in terms of π.

                                       

                                                                     

Example 3:Example 3:Finding the Area of a Sector of a

Circle

100°

AA

CCBB

2

360r

mAB

6 m

2)6(360100

10

A part of a circle bounded by an arc and the segment A part of a circle bounded by an arc and the segment joining its endpoints. joining its endpoints.

To find the area of a segment for a minor arc, draw radii to 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 form a sector. The area of the segment equals the area of the sector minus the area of the triangle formed. the sector minus the area of the triangle formed.                                                                                                                                                                                                                                                                                                                                                                                

SSegment of a Circle

Example 4:Example 4:Finding the Area of a Segment of a

CircleFind the area of the shaded segment. Round your Find the area of the shaded segment. Round your answer to the nearest tenth. answer to the nearest tenth.

                                                                                                                                                                                                                                                                                                                                            

                                                                                                                      

Find the area of sector AOB.Find the area of sector AOB.

Find the area of ∆ AOB.Find the area of ∆ AOB.

Find the area of the segment.Find the area of the segment.

The area of the segment The area of the segment is about 28.5 in.is about 28.5 in.22

Example 5:Example 5:Finding the Area of a Segment of a Circle

A circle has a radius of 24 ft. Find the area of the A circle has a radius of 24 ft. Find the area of the smaller segment of the circle determined by a smaller segment of the circle determined by a

120° arc. Round your answer to the nearest tenth.120° arc. Round your answer to the nearest tenth.

                                                                                                                                                                                                                                                                                                                                            

                                                                                                                      

Find the area of the sector.Find the area of the sector.

Find the area of ∆ AOB.Find the area of ∆ AOB. Find the area of the segment.Find the area of the segment.

The area of the segment The area of the segment is about 353.5 ft.is about 353.5 ft.22

2)24(360120

57631

192

)12)(324(21

4.249

4.249192

24 24120°60°

hyp.= 2•SL

24=2•SL

12=SL

LL=√3•SL

LL=√3•12

LL=12√3

48.353

AssignmentAssignment

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