anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Z4K4R1Y4
  • Z4K4R1Y4
have you done radians?
anonymous
  • anonymous
@Z4K4R1Y4 nope I have no idea what that is

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More answers

Z4K4R1Y4
  • Z4K4R1Y4
|dw:1433038449394:dw| does this make sense?
anonymous
  • anonymous
yes a little thank you @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
so what would be the area of the full circle i've drawn?
Z4K4R1Y4
  • Z4K4R1Y4
\[area= \pi*r ^{2}\]
anonymous
  • anonymous
1256.63? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
yes
Z4K4R1Y4
  • Z4K4R1Y4
now we want to find the sector with angle 120
anonymous
  • anonymous
45238.9342? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
not quite.
Z4K4R1Y4
  • Z4K4R1Y4
full circle = 360 degrees
Z4K4R1Y4
  • Z4K4R1Y4
if we divide 360 by 120 we get three
Z4K4R1Y4
  • Z4K4R1Y4
so that means 120 is 1/3 of 360. right?
anonymous
  • anonymous
Right. :) @Z4K4R1Y4
Z4K4R1Y4
  • 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?
anonymous
  • anonymous
It would be 418.876667? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
Right!!
Z4K4R1Y4
  • Z4K4R1Y4
now for the next part...
Z4K4R1Y4
  • Z4K4R1Y4
|dw:1433039404347:dw|
Z4K4R1Y4
  • Z4K4R1Y4
\[area of full circle = \pi * r ^{2}\] ... but this time r =5
anonymous
  • anonymous
78.5398163? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
yes!
Z4K4R1Y4
  • Z4K4R1Y4
now for the area of the sector of angle 120.
Z4K4R1Y4
  • Z4K4R1Y4
area of full circle (360 degrees) = 78.53... so area of sector of angle 120 would be 1/3 of 78.53...
Z4K4R1Y4
  • Z4K4R1Y4
yh we're caculating the white part of raius 5
Z4K4R1Y4
  • Z4K4R1Y4
*radius
Vocaloid
  • 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
Z4K4R1Y4
  • Z4K4R1Y4
the second diagram is only showing the white part
Z4K4R1Y4
  • Z4K4R1Y4
@alexwaldorf do you under stand the calculation?
Z4K4R1Y4
  • Z4K4R1Y4
@Vocaloid thanks
Vocaloid
  • Vocaloid
yeah, sorry about interrupting, my mistake D:
anonymous
  • anonymous
yes a little lol @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
@Vocaloid Np
anonymous
  • anonymous
it's okay thanks :) @Vocaloid
Z4K4R1Y4
  • Z4K4R1Y4
so what would be the area of the sector in the second part? @alexwaldorf
anonymous
  • anonymous
19374.08? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
not quite. area of full circle = 78.53982.. area of sector of angle 120 would be 1/3 of that.
anonymous
  • anonymous
oh so is it 23.17994? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
yes!... do you understand why it's 1/3 of full area?
anonymous
  • anonymous
26*
anonymous
  • anonymous
yes I do :) @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
good. finally we have...
Z4K4R1Y4
  • Z4K4R1Y4
|dw:1433040636347:dw|
Z4K4R1Y4
  • Z4K4R1Y4
area of sector of radius 20 (15+5) = 418.87.. and area of sector of radius 5 (white part) = 23.17...
Z4K4R1Y4
  • Z4K4R1Y4
does that make sense?
anonymous
  • anonymous
yes it does
anonymous
  • anonymous
so is 23.17 the answer?
anonymous
  • anonymous
@Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
not quite. the area we need to find is the black part.
Z4K4R1Y4
  • Z4K4R1Y4
|dw:1433041243267:dw|
Z4K4R1Y4
  • Z4K4R1Y4
@alexwaldorf ??
anonymous
  • anonymous
395.695? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
that is correct but if you put all the decimals in from both calculations you will get 392.6990817.
anonymous
  • anonymous
so is that the final answer lol @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
yes
anonymous
  • anonymous
so we're done that's it?? @Z4K4R1Y4
Z4K4R1Y4
  • Z4K4R1Y4
yes
anonymous
  • anonymous
oh my goodness thank you so much you're the best @Z4K4R1Y4 I really really appreciate it
Z4K4R1Y4
  • Z4K4R1Y4
no problem. you're welcome
Z4K4R1Y4
  • Z4K4R1Y4
I've got to go now...bye
anonymous
  • anonymous
have a great night, thanks a bunches!! @Z4K4R1Y4

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