11.5 areas of circles and sectors

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11.5 Areas of Circles and Sectors CA State Standards 8: Solve problems involving perimeter and area. 19: Use trigonometric functions 21. Prove and solve problems regarding circle parts. Lesson Goals Find the area of a sector. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

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11.5 Areas of Circles and Sectors. CA State Standards. Lesson Goals. Find the area o f a sector. 8 : Solve problems involving perimeter and area. 19: Use trigonometric functions 21. Prove and solve problems regarding circle parts. ESLRs: Becoming Effective Communicators, - PowerPoint PPT Presentation

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Page 1: 11.5 Areas of Circles and Sectors

11.5 Areas of Circles and Sectors

CA State Standards8: Solve problems involving

perimeter and area.

19: Use trigonometric functions

21. Prove and solve problems regarding circle parts.

Lesson Goals Find the area of a

sector.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Page 2: 11.5 Areas of Circles and Sectors

theoremArea of a Circle:

Area of a circle is still measured in square units.

r

2A r

Page 3: 11.5 Areas of Circles and Sectors

definitionSector of a Circle

The region bounded by two radii and their intercepted arc. (like a piece of pie)

r

Page 4: 11.5 Areas of Circles and Sectors

Area of a SectorThe ratio of the area A of a sector of a circle to the area of the

circle is equal to the ratio of the measure of the intercepted arc to 360°.

or

Theorem

C B

A

Page 5: 11.5 Areas of Circles and Sectors

2A r

example

Find the area of the circle

3 m

29 mA

23A

Page 6: 11.5 Areas of Circles and Sectors

exampleFind the area of the circle

18 ft2A r

281 ftA

29A

Page 7: 11.5 Areas of Circles and Sectors

exampleFind the area of the sector

X

Z

Y

11 m

2area sector

360

mYZXYZ r

2135360area sector 11XYZ

3638 3

8 121

135o

2142.5 m

Page 8: 11.5 Areas of Circles and Sectors

exampleFind the area of the sector

24579 cm

R M

L

150o

50 cm

712 2500

N

243753 cm

2area sector

360

mLMLRNM r

2210360 50

Page 9: 11.5 Areas of Circles and Sectors

example

 

8.5 mr

Page 10: 11.5 Areas of Circles and Sectors

example

2

Find the diamter of given the area of the

shaded region is 28.3 cm .

C

 

Page 11: 11.5 Areas of Circles and Sectors

Today’s Assignmentp. 695: 3 – 9, 17, 18, 21, 22, 33

Page 12: 11.5 Areas of Circles and Sectors
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