Question

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.

Answer 1

have you done radians?

Answer 2

@Z4K4R1Y4 nope I have no idea what that is

Answer 3

does this make sense?

Answer 4

yes a little thank you @Z4K4R1Y4

Answer 5

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

Answer 6

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

Answer 7

1256.63? @Z4K4R1Y4

Answer 8

yes

Answer 9

now we want to find the sector with angle 120

Answer 10

45238.9342? @Z4K4R1Y4

Answer 11

not quite.

Answer 12

full circle = 360 degrees

Answer 13

if we divide 360 by 120 we get three

Answer 14

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

Answer 15

Right. :) @Z4K4R1Y4

Answer 16

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?

Answer 17

It would be 418.876667? @Z4K4R1Y4

Answer 18

Right!!

Answer 19

now for the next part...

Answer 20

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

Answer 21

78.5398163? @Z4K4R1Y4

Answer 22

yes!

Answer 23

now for the area of the sector of angle 120.

Answer 24

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

Answer 25

yh we're caculating the white part of raius 5

Answer 26

*radius

Answer 27

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

Answer 28

the second diagram is only showing the white part

Answer 29

@alexwaldorf do you under stand the calculation?

Answer 30

@Vocaloid thanks

Answer 31

yeah, sorry about interrupting, my mistake D:

Answer 32

yes a little lol @Z4K4R1Y4

Answer 33

@Vocaloid Np

Answer 34

it's okay thanks :) @Vocaloid

Answer 35

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

Answer 36

19374.08? @Z4K4R1Y4

Answer 37

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

Answer 38

oh so is it 23.17994? @Z4K4R1Y4

Answer 39

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

Answer 40

26*

Answer 41

yes I do :) @Z4K4R1Y4

Answer 42

good. finally we have...