Length and Pm

7.Area of Sectors and Segments.notebook

Arcs, Sectors and Segments

March 27, 2012

Arc - part of a circle's circumference - measured in degrees or length units.

Mar 17­10:25 AM

Length of an Arc =

Mar 17­10:28 AM

Example:
Determine the length of arc AB.
A

80

Pull

m = measure of central angle in degrees 5 cm

B
0

r = radius of circle

Mar 17­10:30 AM

Mar 17­10:33 AM

1

7.Area of Sectors and Segments.notebook

Sector -

part of a circle formed by two radii and an arc.

March 27, 2012

Area of a Sector =

m = measure of central angle in degrees r = radius of circle

Mar 17­10:41 AM

Example:
Determine the area of the sector.

11

mm

Example:
Determine the area of the sector.

Mar 17­10:46 AM

1200

3000

Diameter = 35 m

Mar 17­10:47 AM

Mar 17­10:57 AM

2

7.Area of Sectors and Segments.notebook

Find the area of the shaded sector.

Jul 4­9:27 PM

The beam from a lighthouse reaches a distance of 8 kilometres and spreads to an angle of 35°.
Calculate the area covered by the beam from the lighthouse. Mar 17­3:40 PM

March 27, 2012

The radar beam sent out by an aeroplane reaches a distance of 120 kilometres and covers an angle of 150°.
Calculate the area covered by the beam.

Mar 17­3:42 PM

A windscreen wiper is 45 centimetres long. In one sweep it turns through an angle of 115°.
Calculate the distance it covers in one sweep.

Mar 17­3:43 PM

3

7.Area of Sectors and Segments.notebook

The path traced by a golfer‛s club when he hits the ball is an arc of a circle.
If the golf club is 95 cm long, calculate the distance travelled when the golfer swings his club. Mar 17­3:44 PM

March 27, 2012

Segment part of a circle formed by a chord and its intercepted arc.

Mar 17­11:00 AM

Find the area of the following segment.
Area of a Segment =
Area of the Sector - Area of the triangle
Area of a Triangle:

or

Mar 17­11:01 AM

Mar 17­11:30 AM

4

7.Area of Sectors and Segments.notebook

March 27, 2012

Area of a Sector =

Mar 17­2:42 PM

Mar 17­11:29 AM

A =