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Area of a Sector and Length of an arc

Area of a Sector and Length of an arc. Ms N. Kearney. Major Arc. O. . A. B. Minor Arc. ARCS and SECTORS of CIRCLES. 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.

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Area of a Sector and Length of an arc

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  1. Area of a Sector and Length of an arc Ms N. Kearney

  2. Major Arc O  A B Minor Arc ARCS and SECTORS of CIRCLES 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. Major Sector Minor Sector

  3. Calculating arc lengths of Circles Example 1: Calculate the lengths of the minor and major arcs AB for the circle shown. O 5 cm 115o A B

  4. Calculate the lengths of the minor and major arcs in each case (to 1 dp) 2 1 3 O O O 2.3 cm 3 cm 9 cm 88o 155o 75o 4 5 6 2.4 m O O 1.3 m 130o 312o 215o 7 cm Minor arc = 11.8 cm Minor arc = 8.1 cm Minor arc = 3.5 cm Major arc = 44.8 cm Major arc = 10.7 cm Major arc = 10.9 cm Minor arc = 15.9 cm Minor arc = 3.3 m Minor arc = 2.0 m Major arc = 28.1 cm Major arc = 4.9 m Major arc = 13.1 m

  5. Homework 16/05/11 Powerpoint Questions Q’s 1 – 4 Find the area of each sector and the length of each Arc.

  6. Find the area of this sector? 72° 5 cm

  7. Area of the sector = × π × 52 72° × π × 52 360° 1 5 Find the area of this sector? 72° 5 cm = 15.7 cm2

  8. Calculating sector areas of Circles Example 1: Calculate the areas of the minor and major sectors for the circle shown. O 5 cm 115o A B

  9. Calculate the minor and major sector areas in each case (to 1 dp) 2 1 3 O O O 2.3 cm 3 cm 9 cm 88o 155o 75o 4 5 6 2.4 m O O 1.3 m 130o 312o 215o 7 cm Minor sector = 4.1 cm2 Minor sector = 12.2 cm2 Minor sector = 53.0 cm2 Major sector = 12.6 cm2 Major sector = 16.1 cm2 Major sector = 201.5 cm2 Minor sector = 55.6 cm2 Minor sector = 2.1 m2 Minor sector = 2.4 m2 Major sector = 98.3 cm2 Major sector = 3.2 m2 Major sector = 15.7 m2

  10. 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. Now try this one. 100o 8.4 cm 3 .1 m 160o

  11. Homework 17/05/11  Trigonometry hand out Pg. 379 – 380 Q’s 1 and 2

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