6.8 Areas of Circles & 6.8 Areas of Circles & SectorsSectors

p. 230p. 230

Thm 6.20Thm 6.20 – – Area of a CircleArea of a Circle – –

A = A = rr22

* Remember to square the radius 1* Remember to square the radius 1stst, , then multiply by then multiply by !!

ExEx: Find the area of circle C.: Find the area of circle C.

A = A = rr22

A = A = (3)(3)22

A = 9A = 9 cm cm22

OROR

28.27 cm28.27 cm22CC

3 cm3 cm

ExEx: Find the diameter of circle C : Find the diameter of circle C if the area is 16if the area is 16 ft ft22..

A = A = rr22

1616 = = rr22

16 = r16 = r22

ðð16 = r16 = r

4 ft = r4 ft = r

So,So,

d = 8 ft.d = 8 ft.

Sector of a CircleSector of a Circle• The region bounded by 2 radii & their The region bounded by 2 radii & their

intercepted arc.intercepted arc.

SectorSector

Also aAlso a

sectorsector

• Visually, it might remind you of a slice Visually, it might remind you of a slice of pizza or a piece of pie.of pizza or a piece of pie.

Thm 6.21Thm 6.21 – – Area of a SectorArea of a Sector – –

2

360

r

measurearcA

o

ExEx: Find the area of the small sector : Find the area of the small sector shown.shown.

135135oo11 m11 m

2

360

r

measurearcA

o

211360

135 o

o

A

121360

135A

2 55.142 mA

ExEx: L & M are 2 pts. on a circle R with : L & M are 2 pts. on a circle R with r=50 cm & mr=50 cm & mLRM=150LRM=150oo. Find the areas . Find the areas

of the sectors formed by of the sectors formed by LRM.LRM.

2

360

r

measurearcA

oI

150150oo

II

IIII

2

360

r

measurearcA

oII

250360

150 IA

2 49.3272 cmAI

250360

210 IIA

2 49.4581 cmAII

LLMM

RR 50 cm50 cm