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An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot b

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Bunuel
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An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot b [#permalink] New post   24 Mar 2019, 22:51
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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) \(80 + 10\pi\)

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Re: An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot b [#permalink] New post   25 Mar 2019, 01:18
Bunuel wrote:

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) \(80 + 10\pi\)

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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 \(80 - 20\pi\)
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Re: An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot b [#permalink] New post   25 Mar 2019, 23:31
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
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Re: An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot b [#permalink] New post   27 Mar 2019, 18:54
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Bunuel wrote:

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) \(80 + 10\pi\)

Show Spoiler
Attachment:
cbe2bb4966beb1c1cbc889938c8e120b7d80639b.png


We see that a total of (8 x 10)/1 = 80 tiles are used.

Let’s first determine the shaded portion of just one tile. We see that the radius of the circle from which the quarter circles are formed is ½.

The total area of the 4 quarter circles is 4[1/4 x (1/2^2 x π)] = π/4, so the total area of the shaded region is:.

80 - 80 x π/4 = 80 - 20π

Answer: A
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Re: An 8-foot by 10-foot floor is tiles with square tiles of size 1 foot b [#permalink]
27 Mar 2019, 18:54
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