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An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot by 1 foot. Each tile has a pattern consisting of four white quarter circles of radius 1/2 foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?
(A) \(80 - 20\pi\)
(B) \(60 - 10\pi\)
(C) \(80 - 10\pi\)
(D) \(60 + 10\pi\)
(E) \(80 + 10\pi\)
Attachment:
cbe2bb4966beb1c1cbc889938c8e120b7d80639b.png [ 4.68 KiB | Viewed 4639 times ]
Archit3110
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25 Mar 2019, 01:18
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Bunuel
area of floor = 8*10 = 80
and 4 quarter circle = 4* 1/4 * pi * ( 1/2)^2 = 1/4 pi
area of square =1 and so 1-1/4 * pi
80 *(1-1/4 * pi )
IMO A \(80 - 20\pi\)
25 Mar 2019, 23:31
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Area of Tile = 1 square foot
Area of shaded part for 1 tile= 1-area of circle =1- Pi/4
shaded Area for 80 tiles = 80 ( 1-Pi/4) = 80-20Pi
Area of shaded part for 1 tile= 1-area of circle =1- Pi/4
shaded Area for 80 tiles = 80 ( 1-Pi/4) = 80-20Pi
