1. 11.6 Arc Lengths and Areas of Sectors
Geometry
11.6 Arc Lengths and Areas of Sectors

2. Arc Length The length of part of the circumference.
The length of the arc depends on what two things?
1) The measure of the arc.
2) The size of the circle.
An arc length measures distance while
the measure of an arc is in degrees.

3. Sector of a circle
A region bounded by 2 radii and an arc. .

4.  Portions of a Circle: Determine the Arc measure based on the portion given.
1/3 of circumference :
6π out of a total 36π on the circle:
¼ ● 360
½ ● 360
1/3 ● 360
1/6 ● 360

5. Area of a Sector Formula
measure of the central angle or arc m
πr2
Area of a sector =
360
The area of the entire circle!
The fraction of the circle! .

6. m 2πr 360 . Arc Length Formula measure of the central angle or arc
The circumference of the
entire circle!
2πr
Arc Length =
360
The fraction of the circle! .

7. Find the length of AB and the area of sector AOB.1. 2. 3. 4. 5.
Length of AB
Area of sector AOB B
90o B
90o
240o
300o 12
120o
108o O B O A A O A A 6 12 O
2.4 O
10√2 B B
Fraction of circle:
Fraction of circle:
Fraction of circle:
Fraction of circle:
Fraction of circle:
2/3
5/6
1/3
3/10
Fraction ● circumference
Fraction ● circumference
Fraction ● circumference
¼ ● 12π
2/3 ● 24π
5/6 ● 24π
1/3 ● 4.8π
3/10 ● 20√2π
3π units
16π units
20π units
1.6π units
6√2π units
Fraction ● area
Fraction ● area
Fraction ● area
Fraction ● area
Fraction ● area
¼ ● 36π
2/3 ● 144π
5/6 ● 144π
1/3 ● 5.76π
3/10 ● 200π
9π units2
96π units2
120π units2
1.92π units2
60π units2

8. 6. The area of sector AOB is 48π and
. Find the radius of ○O. m
πr2
Area of a sector =
360
270
48π =
πr2
360 4 16 3 4 r2
48 = 3 4 3 r2
64 = r
= 8

9. 7. The area of sector AOB is
and
. Find the radius of ○O. m
πr2
Area of a sector =
360 9 40
π =
πr2 4
360 9 9 1 9 = r2 1 4 9 1 81 = r2 4 9
r = 2

10. Find the area of the shaded region
Find the area of the shaded region. Point O marks the center of the circle. 8. 9.
10.
11.
60˚ 8 12
60 O 6 4
30 O O
160
π units2
9π - 18 units2
24π - 36√3 units2
8π - 8√3 units2 3

11. HW
P WE #1-19

12. Some common fractions and measures!
Arc or Central Angle Measure
Fraction of the Circle
36o
108o
1/6
5/6
120o
2/3
30o
11/12
1/8
5/8
3/10
1/10
60o
300o
1/3
240o
1/12
330o
45o
225o