## anonymous one year ago A certain windshield wiper clears a portion of a sector as shown. If the angle that the wiper pivots during each swing is 120°, find the area of the windshield that is cleaned during each swing.

1. anonymous

2. Z4K4R1Y4

3. anonymous

@Z4K4R1Y4 nope I have no idea what that is

4. Z4K4R1Y4

|dw:1433038449394:dw| does this make sense?

5. anonymous

yes a little thank you @Z4K4R1Y4

6. Z4K4R1Y4

so what would be the area of the full circle i've drawn?

7. Z4K4R1Y4

$area= \pi*r ^{2}$

8. anonymous

1256.63? @Z4K4R1Y4

9. Z4K4R1Y4

yes

10. Z4K4R1Y4

now we want to find the sector with angle 120

11. anonymous

45238.9342? @Z4K4R1Y4

12. Z4K4R1Y4

not quite.

13. Z4K4R1Y4

full circle = 360 degrees

14. Z4K4R1Y4

if we divide 360 by 120 we get three

15. Z4K4R1Y4

so that means 120 is 1/3 of 360. right?

16. anonymous

Right. :) @Z4K4R1Y4

17. Z4K4R1Y4

so if the area of full circle (angle 360) is 1256.63 then the area of the sector of angle 120 would be 1/3 of 1256.63. right?

18. anonymous

It would be 418.876667? @Z4K4R1Y4

19. Z4K4R1Y4

Right!!

20. Z4K4R1Y4

now for the next part...

21. Z4K4R1Y4

|dw:1433039404347:dw|

22. Z4K4R1Y4

$area of full circle = \pi * r ^{2}$ ... but this time r =5

23. anonymous

78.5398163? @Z4K4R1Y4

24. Z4K4R1Y4

yes!

25. Z4K4R1Y4

now for the area of the sector of angle 120.

26. Z4K4R1Y4

area of full circle (360 degrees) = 78.53... so area of sector of angle 120 would be 1/3 of 78.53...

27. Z4K4R1Y4

yh we're caculating the white part of raius 5

28. Z4K4R1Y4

29. Vocaloid

alright, just making sure, I saw your diagram had the arrow pointing to the black part as the part not cleared by the wiper

30. Z4K4R1Y4

the second diagram is only showing the white part

31. Z4K4R1Y4

@alexwaldorf do you under stand the calculation?

32. Z4K4R1Y4

@Vocaloid thanks

33. Vocaloid

yeah, sorry about interrupting, my mistake D:

34. anonymous

yes a little lol @Z4K4R1Y4

35. Z4K4R1Y4

@Vocaloid Np

36. anonymous

it's okay thanks :) @Vocaloid

37. Z4K4R1Y4

so what would be the area of the sector in the second part? @alexwaldorf

38. anonymous

19374.08? @Z4K4R1Y4

39. Z4K4R1Y4

not quite. area of full circle = 78.53982.. area of sector of angle 120 would be 1/3 of that.

40. anonymous

oh so is it 23.17994? @Z4K4R1Y4

41. Z4K4R1Y4

yes!... do you understand why it's 1/3 of full area?

42. anonymous

26*

43. anonymous

yes I do :) @Z4K4R1Y4

44. Z4K4R1Y4

good. finally we have...

45. Z4K4R1Y4

|dw:1433040636347:dw|

46. Z4K4R1Y4

area of sector of radius 20 (15+5) = 418.87.. and area of sector of radius 5 (white part) = 23.17...

47. Z4K4R1Y4

does that make sense?

48. anonymous

yes it does

49. anonymous

50. anonymous

@Z4K4R1Y4

51. Z4K4R1Y4

not quite. the area we need to find is the black part.

52. Z4K4R1Y4

|dw:1433041243267:dw|

53. Z4K4R1Y4

@alexwaldorf ??

54. anonymous

395.695? @Z4K4R1Y4

55. Z4K4R1Y4

that is correct but if you put all the decimals in from both calculations you will get 392.6990817.

56. anonymous

so is that the final answer lol @Z4K4R1Y4

57. Z4K4R1Y4

yes

58. anonymous

so we're done that's it?? @Z4K4R1Y4

59. Z4K4R1Y4

yes

60. anonymous

oh my goodness thank you so much you're the best @Z4K4R1Y4 I really really appreciate it

61. Z4K4R1Y4

no problem. you're welcome

62. Z4K4R1Y4

I've got to go now...bye

63. anonymous

have a great night, thanks a bunches!! @Z4K4R1Y4