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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