Area of a Sector and Length of an arc

Ms N. Kearney

ARCS and SECTORS of CIRCLES

Minor Sector

Major Sector

O

A B

The angle between two radii of a circle divides the circle into a minor and a major sector. The arc lengths of each sector are the minor and major arcs respectively.

Minor Arc

Major Arc

r2

360AB lengtharc x

2

360AOBarea sector r

x

r2360

115arc minor x

Calculating arc lengths of Circles

Example 1: Calculate the lengths of the minor and major arcs AB for the circle shown.

O

A B

115o 5 cm

10360

115arc minor x

r2360

245arc major x

10360

245arc major x

). dpcm (1 010

). dpcm (1 421

Minor arc = 11.8 cm

Major arc = 44.8 cm

Calculate the lengths of the minor and major arcs in each case (to 1 dp)

75o 9 cm 155o3 cm

88o

2.3 cm

130o

7 cm215o

2.4 m

312o

O O O

O O1.3 m

1 2 3

4 5 6

Minor arc = 8.1 cm

Major arc = 10.7 cm

Minor arc = 3.5 cm

Major arc = 10.9 cm

Minor arc = 15.9 cm

Major arc = 28.1 cm

Minor arc = 3.3 m

Major arc = 4.9 m

Minor arc = 2.0 m

Major arc = 13.1 m

Homework 16/05/11

Powerpoint Questions

Q’s 1 – 4

Find the area ofeach sector andthe length of eachArc.

Find the area of this sector?

72°5 cm

Area of the sector =72°

360° × π × 52

1

5 × π × 52

= 15.7 cm2

Find the area of this sector?

72°5 cm

2

360

115area sector minor rx

Calculating sector areas of Circles

Example 1: Calculate the areas of the minor and major sectors for the circle shown.

O

A B

115o 5 cm

25360

115 x

2

360

245area sector major rx

25360

245x

). dpcm (1 125 2

). dpcm (1 553 2

Minor sector = 53.0 cm2

Major sector = 201.5 cm2

Calculate the minor and major sector areas in each case (to 1 dp)

75o 9 cm 155o3 cm

88o

2.3 cm

130o

7 cm215o

2.4 m

312o

O O O

O O1.3 m

1 2 3

4 5 6

Minor sector = 12.2 cm2

Major sector = 16.1 cm2

Minor sector = 4.1 cm2

Major sector = 12.6 cm2

Minor sector = 55.6 cm2

Major sector = 98.3 cm2

Minor sector = 2.1 m2

Major sector = 3.2 m2

Minor sector = 2.4 m2

Major sector = 15.7 m2

48 2360

100 lengtharc .xx

Example Question: The shape below is a sector of a circle of radius 8.4 cm. Find (a) the arc length and (b) sector area.

100o

8.4 cm

248 360

100area sector .xx

dp) (1 cm 714.

dp) (1 cm 661 2.

160o

3 .1 m

Now try this one.

13 2360

160 lengtharc .xx

213 360

160area sector .xx

dp) (1 m 78.

dp) (1 m 413 2.

Homework 17/05/11

Trigonometry hand out

Pg. 379 – 380

Q’s 1 and 2