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The figure shows the design of a mosaic tile in which the fo
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22 Nov 2019, 11:05
22 Nov 2019, 11:05
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55% (02:55) correct
44% (02:37) wrong based on 18 sessions
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#greprepclub The figure shows the design of a mosaic.jpg [ 19.11 KiB | Viewed 9540 times ]
The figure shows the design of a mosaic tile in which the four sides of the square are the diameters of four intersecting semicircles. Small blue stones are to be placed in the shaded regions and will cover 95 percent of the area of these regions. If each side of the square has length 2 feet, approximately how many square feet of the tile will be covered by the blue stones?
A. 0.9
B. 1.5
C. 2.2
D. 2.9
E. 3.2
Kudos for the right answer and solution.
Re: The figure shows the design of a mosaic tile in which the fo
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27 Nov 2019, 13:37
27 Nov 2019, 13:37
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The answer is C.
Let A= Area of one of the shaded areas.
A= 2 X (Area of half of semi circle - Area of right angle triangle)
= 2 X (1/4 X pi X 1^2 - 1/2 X 1 X 1)
= 2 X (1/4 X pi - 1/2)
= 1/2 X pi -1
So area of total shaded region = 4 X A = 4 X (1/2 X pi - 1) = 2 X pi -4
So the required area = 0.95 X (2 X pi -4 ) =0.95 X 2.28 = 2.2
Let A= Area of one of the shaded areas.
A= 2 X (Area of half of semi circle - Area of right angle triangle)
= 2 X (1/4 X pi X 1^2 - 1/2 X 1 X 1)
= 2 X (1/4 X pi - 1/2)
= 1/2 X pi -1
So area of total shaded region = 4 X A = 4 X (1/2 X pi - 1) = 2 X pi -4
So the required area = 0.95 X (2 X pi -4 ) =0.95 X 2.28 = 2.2
Re: The figure shows the design of a mosaic tile in which the fo
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25 Oct 2024, 03:00
25 Oct 2024, 03:00
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