11.3 Area of Circles and Sectors

Section 11.3 ~ Areas of Circles and Sectors

Objectives: Be able to find the area of circles and sectors!!

Quick Review:

Name the following from circle Z.

a) Minor arc:

b) Major arc:

c) Semicircle:

d) Radius:

e) Diameter:

ZL

MNO

ON, NM, ML, OM, NL

OLM, OLN, MNL, MOL, NOL, NOM, NLMOL

OZ, NZ, MZ, LZ

OL

The equation for the Area of a Circle Area equals radius squared times pi.

Theorem

2rA 9

The equation for the Area of a Circle Area equals pi times radius squared.

Theorem

2rA

9

81

9 2

A

A

2rA Area of a Circle!

Find the area of each circle. Leave answers in terms of π.

More Vocab:• Sector of a circle: region bounded by an arc

and the two radii touching its endpoints

sector AOB

A

O

B

14 in. 10 in.12 in.

214A 25A2in.196

26A2in.25 2in.36

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

Definition of a Circle Sector

SectorMinor ManPac

SectorMajor

The Equation for the Area of a Sector

2

360rSector 135

11

The Equation for the Area of a Sector

2

360rSector

13511

375.45

1218

3

11360

135 2

Sector

Sector

)(360

sectorofarea 2 rABarcofmeasure

AXB

Find the area of each sector. Leave answers in terms of π.

a) Sector CZD

b) Sector BZC

c) Sector BZA

220360

72 400360

72 2cm80

220360

18 400360

18 2cm20

ZA

DCB

72°

20 cm

18°

220360

180 400360

180 2cm200

The Sector Area is

Find the Radius

150

𝑆𝑒𝑐𝑡𝑜𝑟=𝜃

360(𝑟2𝜋 )

15𝜋=150360

(𝑟 2)𝜋

15=512𝑟2

𝑟2=15(125

)→36

𝑟2=36→√𝑟2=±√36

𝑟=6

𝟏𝟓𝝅𝑪𝒆𝒏𝒕𝒓𝒂𝒍 𝑨𝒏𝒈𝒍𝒆𝒊𝒔𝟏𝟓𝟎°

15 cm

Challenge Problems!Find the area of each shaded region. Leave answers in terms of π.

10 in.

circlesquareshaded AAA

1010square A 2in.100

2shaded in.25100 A

2circle 5A 2in.25

circlesquareshaded AAA

3030square A 2cm900

2shaded cm225900 A

2circle 15A 2cm225

Do you know your formulas?

Circumference: rd 2

Carcofmeasure

360

2r

Aarcofmeasure

360

Arclength:

Area:

Area of sector: