Transcript 11.5 Areas of Circles & Sectors

6.8 Areas of Circles &
Sectors
p. 230
Thm 6.20 – Area of a Circle –
A = r2
* Remember to square the radius 1st,
then multiply by !
Ex: Find the area of circle C.
C
A = r2
A = (3)2
A = 9 cm2
OR
28.27 cm2
Ex: Find the diameter of circle C
if the area is 16 ft2.
A = r2
16 = r2
16 = r2
ð16 = r
4 ft = r
So,
d = 8 ft.
Sector of a Circle
• The region bounded by 2 radii & their
intercepted arc.
Sector
Also a
sector
• Visually, it might remind you of a slice
of pizza or a piece of pie.
Thm 6.21 – Area of a Sector –
arc measure
2
A


r
o
360
Ex: Find the area of the small sector
shown.
arc measure
2
A
 r
o
360
o
135
2
A
  11
o
360
135o
135
A
121
360
A  142.55 m
2
Ex: L & M are 2 pts. on a circle R with
r=50 cm & mLRM=150o. Find the areas
of the sectors formed by LRM.
arc measure
2
AII 
 r
o
360
arc measure
2
AI 


r
360 o
II
150
2
AI 
  50 
360
210
2
AII 
  50 
360
R
AI  3272.49 cm
2
L
150o
I
M
AII  4581.49 cm
2