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CIRCLE

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CIRCLE. Look at the picture. RELATION BETWEEN THE CENTRAL ANGLE, SECTOR AREA, AND THE LENGHT OF ARCS BETWEEN TWO SECTORS. B. A. 0. B. C. Look at the picture. . A. . O. D. RELATION BETWEEN THE CENTRAL ANGLE, THE LENGHT OF ARCS, and SECTOR AREA. B. . O. A.

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CIRCLE

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  1. CIRCLE

  2. Look at the picture RELATION BETWEEN THE CENTRAL ANGLE, SECTOR AREA, AND THE LENGHT OF ARCS BETWEEN TWO SECTORS B A 0

  3. B C Look at the picture  A  O D RELATION BETWEEN THE CENTRAL ANGLE, THE LENGHT OF ARCS, and SECTOR AREA

  4. B  O A If central angle is compared to a full angle of circle that is ( 3600), then :

  5. B  O A If the central angle that be compared to the full angle of circle ( 3600), then :

  6. B A 500 O 800 D C Example 1 : Look at the picture beside, the lenght of arc AB = 40 cm, AOB = 500, and AOB=800. Find the lenght of arc CD.

  7. B A 500 O 800 D C Solution : Given : AB = 40 cm, AOB = 500, AOB=800 Asking :Find the lenght of arc CD Answer: X = ( 40 x 80 ) : 50 = 64. So, we get the lenght of arc CD = 64 cm

  8. O 540 B A Example 2 : Look at the picture! The lenght of radii = 20 cm, AOB = 540. Determine the area of sector OAB

  9. Solution : Given : AOB = 540, and radii = 20 cm X = ( 3 x 1256 ) : 20 = 188,4 cm2. So, we get the area of sector OAB = 188,4 cm2.

  10. EXERCISE

  11. R O 450 P Q Question - 1 Look at the picture, the lenght of arc PQ = 50 cm, the lenght of arc QR = 75 cm and POQ = 450. Determine QOR.

  12. Solution : Given : The lenght of arc PQ = 50 cm The lenght of arc QR = 75 cm POQ = 450 X = ( 3 x 45) : 2 = 135 : 2 = 67,50 So, we get  QOR = 67,50.

  13. D B 600 O 12 cm A 12 cm C Question - 2 Look at the picture, COD = 600, the lenght of OA = 12 cm and AC = 12 cm. Calculate the area of the shaded region.

  14. Solution : Asking : the area of the shaded region. Given : Radii (1) = 12 cm Radii (2) = 24 cm. AOB = 600 Answer: Area of sector OAB = 60/360 x area of circle = 1/6 x 3,14 x 12 x 12 = 3,14 x 24 = 75,36 cm2

  15. Area of sector OCD = 60/360 x area of circle = 1/6 x 3,14 x 24 x 24 = 3,14 x 96 = 301,44 cm2 The area of the shaded region: = area of sector OCD - area of sector OAB = 301,44 cm2 - 75,36 cm2 = 226,08 cm2.

  16. 42 cm Question - 3 Calculate the area of the shaded region as shown in the figure above !

  17. 42 cm Solution: The area of circle that is shaded : L = ½  r2 = ½ x 22/7 x 21 x 21 = ½ x 22 x 63 = 11 x 63 = 693 cm2 The area of small circle that is shaded = The area of small circle that isn’t shaded.

  18. QUIZ

  19. C O 1200 400 A B Quiz - 1 Look at the picture, the area of sector OAB =60 cm2, AOB = 400 and BOC = 120o Find the area of sector OBC.

  20. 14 cm Quiz - 2 Calculate the area of the shaded region as shown in the figure above !

  21. Solution Quiz 1 : Given : AOB = 400 and BOC = 1200 The area of sector OAB = 60 cm2 Asking: The area of sector OBC. Answer: X = 3 x 60 = 180 cm2. So we get the area of sector OBC = 180 cm2.

  22. 14 cm Solution Quiz 2: The area of circle that is shaded : Lb =  r2 = 22/7 x 7 x 7 = 154 cm2 Lk =  r2 = 22/7 x 3,5 x 3,5 = 38,5 cm2 The area of the shaded region = 154 - 38,5 = 115,5 cm2

  23. I Like Mathematics

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