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.

- anonymous

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- anonymous

##### 1 Attachment

- Z4K4R1Y4

have you done radians?

- anonymous

@Z4K4R1Y4 nope I have no idea what that is

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## More answers

- Z4K4R1Y4

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

- anonymous

yes a little thank you @Z4K4R1Y4

- Z4K4R1Y4

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

- Z4K4R1Y4

\[area= \pi*r ^{2}\]

- anonymous

1256.63? @Z4K4R1Y4

- Z4K4R1Y4

yes

- Z4K4R1Y4

now we want to find the sector with angle 120

- anonymous

45238.9342? @Z4K4R1Y4

- Z4K4R1Y4

not quite.

- Z4K4R1Y4

full circle = 360 degrees

- Z4K4R1Y4

if we divide 360 by 120 we get three

- Z4K4R1Y4

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

- anonymous

Right. :) @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

It would be 418.876667? @Z4K4R1Y4

- Z4K4R1Y4

Right!!

- Z4K4R1Y4

now for the next part...

- Z4K4R1Y4

|dw:1433039404347:dw|

- Z4K4R1Y4

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

- anonymous

78.5398163? @Z4K4R1Y4

- Z4K4R1Y4

yes!

- Z4K4R1Y4

now for the area of the sector of angle 120.

- Z4K4R1Y4

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

- Z4K4R1Y4

yh we're caculating the white part of raius 5

- Z4K4R1Y4

*radius

- 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

the second diagram is only showing the white part

- Z4K4R1Y4

@alexwaldorf do you under stand the calculation?

- Z4K4R1Y4

@Vocaloid thanks

- Vocaloid

yeah, sorry about interrupting, my mistake D:

- anonymous

yes a little lol @Z4K4R1Y4

- Z4K4R1Y4

@Vocaloid Np

- anonymous

it's okay thanks :) @Vocaloid

- Z4K4R1Y4

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

- anonymous

19374.08? @Z4K4R1Y4

- Z4K4R1Y4

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

- anonymous

oh so is it 23.17994? @Z4K4R1Y4

- Z4K4R1Y4

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

- anonymous

26*

- anonymous

yes I do :) @Z4K4R1Y4

- Z4K4R1Y4

good. finally we have...

- Z4K4R1Y4

|dw:1433040636347:dw|

- Z4K4R1Y4

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

- Z4K4R1Y4

does that make sense?

- anonymous

yes it does

- anonymous

so is 23.17 the answer?

- anonymous

@Z4K4R1Y4

- Z4K4R1Y4

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

- Z4K4R1Y4

|dw:1433041243267:dw|

- Z4K4R1Y4

@alexwaldorf ??

- anonymous

395.695? @Z4K4R1Y4

- Z4K4R1Y4

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

- anonymous

so is that the final answer lol @Z4K4R1Y4

- Z4K4R1Y4

yes

- anonymous

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

- Z4K4R1Y4

yes

- anonymous

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

- Z4K4R1Y4

no problem. you're welcome

- Z4K4R1Y4

I've got to go now...bye

- anonymous

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

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