Derive the formulas for sector area and arc length Solve problems involving sector area and arc length

1. Sector Area & Arc Length
The student is able to (I can):
• Develop and use formulas to find arc length and sector
area of circlesarea of circles

2. chord
arc
A line segment whose endpoints are on the
circle.
A portion of a circle.
K
•
K
EEEE Y
KY is a chord.
KY is an arc.

3. arc measure
arc length
The measure of the central angle that
intercepts the arc.
The distance along an arc. It is
proportional to the circumference of the
circle.
arc length central angle
circumference 360
=
°
•
mºmºmºmº
m
L C
360
° =  
° 
where C is the
circumference (either
C=πd or C=2πr).
mº

4. Example Find each exact arc length.
1.
120º
• 3333′′′′
( )
120
L 2 3
360
 = π  
 
2 ft.= π
2.
72º72º72º72º
8 m8 m8 m8 m ( )
72
L 2 8
360
 = π  
 
16
or 3.2 m
5
= π π
•

5. central angle
of a circle
sector of a
circle
An angle whose vertex is on the center of
the circle, and whose sides intersect the
circle.
A region bounded by a central angle.
R
•AAAA
G
∠RAG is a central angle
RAG is a sector

6. The area of a sector is proportional to the
area of the circle containing the sector.
Area of sector central angle
Area of circle 360
=
°
°
=
π °2
S m
r 360
° m° = π  
° 
2 m
S r
360
Formula:

7. Examples Find the area of each sector. Leave
answers in terms of π.
1.
•
120º 2"2"2"2"
( )2 120
S 2
360
°
= π
°
4 120
360
 = π 
 
i
24
in.
3
= π
2.
• 72º
10m10m10m10m
in.
3
= π
( )2 72
S 10
360
° = π  
° 
7200
360
 = π 
 
2
20 m= π