Keystone GeometryArc Length and Area of a Sector
A sector of a circle is a region bounded by two radii and an arc of the circle. The area of the sector is a fraction of the area of a circle. The arc length that bounds the sector
is a fraction of the circumference of the circle.
Area of sector AOB
x360
r2
xLength of AB 2 r360
Sector of a Circle
Arc LengthArc length is the distance around an arc .
The circumference multiplied by the ratioof the center angle and 360º.
Formula:
Example: Arc Length
Example
4
a
3602r
72360
24
Example:
4 cm
72 °
BC
A
0.8 2.51 cm
Find the Arc Length of AC if the central angle is 72 degrees and circle B has a radius of 4 cm.
AC
Paper FansO In the blue
fan, find the length of arc AB
5
O In the green fan, find the length of arc CD
O In the red fan, find the length of arc EF
Tires
6
Area of a SectorArea of a sector is the area of a section of the circle.
It is a fraction of the entire area that is dependent upon the size of the central angle.
The area multiplied by the ratio of the center angle and 360°
Formula:
Example: Sector
Example
1.625 5.11 cm2
Example: Find the area of a sector if the Central angle is 65 degrees and the radius of the circle is 3 cm.
Example:
65°
Sector
a
360r 2
65
36032
Paper FanO A stretched out paper fan forms a sector
with a radius of 18 cm and an angle of 175⁰. Calculate the area of the stretched out fan. Give your answer to 1 decimal place.
9
Windshield WipersO A window wiper of length 20 inches goes
through an angle of 160⁰. Work out the area of window covered by the window wiper.
10
1. 2. 3. 4.
Sector AOB is described by giving m AOBand the radius of circle O. Find the length
of and the area of sector AOB. Use 3.14for . Round to the nearest tenth.
AB
Find the area of the shaded region. Point M marks the center of a circle. Leave your answers in terms of Pi.
A
6
A
4
60
M M
In a circle with radius 6, mAB 108.Make a sketch and find the area of
the region bounded by AB and AB.
Round each answer to the nearest tenth.
Round each answer to the nearest tenth.