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After a one-piece circular tablecloth of maximum possible area was cut
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23 May 2020, 08:37
23 May 2020, 08:37
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A
B
C
D
E
Difficulty:
25%
(medium)
Question Stats:
70% (01:15) correct
30%
(01:11)
wrong
based on 402
sessions
After a one-piece circular tablecloth of maximum possible area was cut from a rectangular piece of material, what was the number of square inches of material that remained?
(1) The piece of material was 48 inches wide and 56 inches long before the tablecloth was cut.
(2) The radius of the tablecloth was 24 inches.
DS20411
(1) The piece of material was 48 inches wide and 56 inches long before the tablecloth was cut.
(2) The radius of the tablecloth was 24 inches.
DS20411
After a one-piece circular tablecloth of maximum possible area was cut
[#permalink]
08 Jan 2022, 02:49
08 Jan 2022, 02:49
1
Kudos
kartikeysharma
I'm sorry, but the solution is still not clear to me. How is the answer A and not C?
We only know that the figure is a rectangle.
We don’t know whether the rectangle is a square or not.
The circle we can draw within a rectangle will be limited by the shorter side (here the circle must stay within the boundaries of the rectangle)
Imagine a circle with diameter 4.
The MAX Area circle we could draw would be perfectly inscribed within a square with equal side lengths of 4.
Now imagine the square is stretched along its length.
We now have a rectangle with width = 4 and the length = 100
Again, the MAX circle we can draw within this rectangle will have a diameter of 4: the same circle as in the case of the square with side length 4.
The circle is a set of equidistant points from the center. Hence, no matter how we tried to draw the circle, we are limited by the shorter side of the rectangle.
Hope that helps a bit? 🙂
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Re: After a one-piece circular tablecloth of maximum possible area was cut
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23 May 2020, 10:41
23 May 2020, 10:41
To maximize the area of the circle, diameter of the cloth = d = min(a,b) , where a and b are the sides of the rectangular piece
Area of remaining portion = \(a*b - \frac{\pi*d^2}{4 }\)
Statement 1=
We know a and b; hence we can find d.
Sufficient
Statement 2-
We know d; hence we can find the shorter side of the rectangle. We have no idea about the longer side.
Insufficient
Area of remaining portion = \(a*b - \frac{\pi*d^2}{4 }\)
Statement 1=
We know a and b; hence we can find d.
Sufficient
Statement 2-
We know d; hence we can find the shorter side of the rectangle. We have no idea about the longer side.
Insufficient
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