11.5 area of circles and sectors. theorem the equation for the area of a circle area equals radius...

11.5 Area of Circles and Sectors

Theorem

The equation for the Area of a Circle

Area equals radius squared times pi.

2rA

9

Theorem

The equation for the Area of a Circle

Area equals radius squared times pi.

2rA

9

81

9 2

A

A

Definition of a Circle Sector

A circle sector is a fraction of the circle enclosed by two radii and an arc.

SectorMinor ManPac

SectorMajor

Theorem

The Equation for the Area of a Sector

2

360rSector

13511

TheoremThe Equation for the Area of a Sector

2

360rSector

13511

375.45

1218

3

11360

135 2

Sector

Sector

Find the Radius

The Sector Area is 15015 AngleCentral

2

2

360

15015

360

r

rSector

150

Find the Radius


2

2

2

12

515

360

15015

360

r

r

rSector

150

Find the Radius


2

2

2

12

515

360

15015

360

r

r

rSector

150

3636

365

1215

22

2

rr

r

Find the Radius


2

2

2

12

515

360

15015

360

r

r

rSector

150

6

3636

365

1215

22

2

r

rr

r

Find the Shaded Area

Hint : find the Area of the Circle – the Area of the triangle

60 60

60

4

4

4



60 60

60

4

4

4

2 2

xx2

32 x30

3

42

3

222

3

2

rx

x



60 60

60

4

4

4

2 2

3

16

3

4

circletheofArea

34344

1

34

1

2

2

A

sidetriagnleofArea



60 60

60

4

4

4

2 2

3

16

3

4

circletheofArea

34344

1

34

1

2

2

A

sidetriagnleofArea

343

16 areaRED

Homework

Page 695-698

# 10 – 28 even,

31 – 37, 40, 41,

43 - 44

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