Arc length and the area of sectors

Word problem

Objectives:

•To find the arc length and area of sectors

•“Clover Leaf ” interchanges on freeways contain four sectors.

Architecture

•Computer hard drives store information in areas called sectors.

Any work field associat-ed with using computers

Race track designers

•Certain measurements are required for the arc.

Pie charts

•A pie chart is a circular chart divided into triangular areas.

Art

Dart board

•To find the length of an arc:

•To find the area of a sector:

Q7 page 276

A flower bed is a quadrant of a circle.a) Find the length of edging needed for the

curved edge of the bed.b) Find the area of the flower bed.

1.9

m

1.9m

a)Length of arc

= 90 x 2 x 3.14 x 1.9= 2.983

Length of edging needed= 2.983m

360

b) Area of sector

= 90 x 3.14 x 1.9 x 1.9= 2.83385

Area of the flower bed= 2.83385m

3602

Try this

A silver earring pendant is part of a sector of a circle. Find the area of the silver.

Area of the entire sector=60 x 3.14 x 16 x 16=360

133.973mm2

Area of the white part=60 x 3.14 x 12 x 12=360

75.36mm2

Area of the silver part=

= 58.613mm2

A of the entire sector – A of the white part

= 133.973 – 75.36

More questions1)Radius: 48cm,Angle at centre: 70a) Find the arc length.b) Calculate the area of the given sector.

2) A pumpkin pie is made in a mini pie pan measuring 5 inches in diameter. It is cut into 4 equal slices. What is the area of one piece of the pie?

O