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.