11.5 areas of circles and sectors
DESCRIPTION
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 PresentationTRANSCRIPT
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
theoremArea of a Circle:
Area of a circle is still measured in square units.
r
2A r
definitionSector of a Circle
The region bounded by two radii and their intercepted arc. (like a piece of pie)
r
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
2A r
example
Find the area of the circle
3 m
29 mA
23A
exampleFind the area of the circle
18 ft2A r
281 ftA
29A
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
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
example
8.5 mr
example
2
Find the diamter of given the area of the
shaded region is 28.3 cm .
C
Today’s Assignmentp. 695: 3 – 9, 17, 18, 21, 22, 33