Transcript 11.5 Area of Circles and Sectors

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: ON, NM, ML, OM, NL
O
OLM,
OLN,
MNL,
MOL,
b) Major arc:
N
NOL, NOM, NLM
c) Semicircle: OL
d) Radius: OZ, NZ, MZ, LZ
e) Diameter: OL
Z
L
M
Theorem
The equation for the Area of a Circle
Area equals radius squared times pi.
A  r
2
9
Theorem
The equation for the Area of a Circle
Area equals pi times radius squared.
A  r
2
A   9 
2
A  81
9
Area of a Circle!A  r 2
Find the area of each circle. Leave answers in terms of π.
14 in.
10 in.
12 in.
A   14 2
 196 in.2
A    52
 25 in.2
A    62
 36 in.2
More Vocab:
A
• Sector of a circle: region bounded by an arc
and the two radii touching its endpoints
sector
AOB
B
O
Definition of a Circle Sector
A circle sector is a fraction of the circle enclosed by two
radii and an arc.
Minor Sector
Major Sector
Pac  Man 
The Equation for the Area of a Sector
Sector 

360
r  
2
135 
11
The Equation for the Area of a Sector
Sector 

360
r  
2
135 2
11  
Sector 
360
3
Sector  121 
8
 45.375
135 
11
measure of arc AB
area of sector AXB 
 (r 2  )
360
Find the area of each sector. Leave answers in terms of π.
a) Sector CZD
72
72
2
 400   80 cm2

 20   
360
360
b) Sector BZC
18
18
2

 20   
 400   20 cm2
360
360
c) Sector BZA
180
180
2

 20   
 400   200 cm 2
360
360
A
Z
B
18°
C
20 cm
D
72°
Find the Radius
The Sector Area is 𝟏𝟓𝝅 𝑪𝒆𝒏𝒕𝒓𝒂𝒍 𝑨𝒏𝒈𝒍𝒆 𝒊𝒔 𝟏𝟓𝟎°
𝜃
𝑆𝑒𝑐𝑡𝑜𝑟 =
(𝑟 2 𝜋)
360
15𝜋 =
150 
150 2
(𝑟 )𝜋
360
5 2
15 =
𝑟
12
12
𝑟 = 15( ) → 36
5
2
𝑟 2 = 36 →
𝑟 2 = ± 36
𝑟=6
Challenge Problems!
Find the area of each shaded region. Leave answers in terms of π.
10 in.
Ashaded  Asquare  Acircle
15 cm
Ashaded  Asquare  Acircle
Asquare  1010  100in.2
Asquare  30 30  900cm2
Acircle  52    25 in.2
Acircle  152    225 cm2
Ashaded  100 25 in.2
Ashaded  900 225 cm2
Do you know your formulas?
Circumference: d  2r
Arclength:  measure of arc  C
360
Area:  
r2
measure of arc
Area of sector: 
A
360