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Suppose five circles, each 4 inches in diameter, are cut fro

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Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   25 Mar 2019, 11:41
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Suppose five circles, each 4 inches in diameter, are cut from a rectangular strip of paper 12 inches long. If the least amount of paper is to be wasted, what is the width of the paper strip?

(A) \(5\)

(B) \(4+2\sqrt{3}\)

(C) \(8\)

(D) \(4(1+ \sqrt{3})\)

(E) not enough information
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B
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JelalHossain
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Re: Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   09 May 2019, 06:29
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5*4Pi/12=possible width of the rectangle
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shreyaguha005
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Re: Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   12 Aug 2020, 04:49
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JelalHossain wrote:
5*4Pi/12=possible width of the rectangle



Can you provide the solution please?
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Re: Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   12 Aug 2020, 05:29
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To have the strip at its maximum height the figure looks like the following

Attachment:
GRE circles.png
GRE circles.png [ 2.53 KiB | Viewed 2883 times ]


The circles are connected at the centers thanks to an equilateral triangle


Attachment:
GRE circles (2).png
GRE circles (2).png [ 4.39 KiB | Viewed 3075 times ]


H is the following

Attachment:
GRE circles (3).png
GRE circles (3).png [ 1.63 KiB | Viewed 3111 times ]


so the height is \(h=2\sqrt{3}\)


Adding to this the distances on top and at the bottom of the triangle


Attachment:
GRE circles (4).png
GRE circles (4).png [ 4.83 KiB | Viewed 3111 times ]


we do have \(4+2\sqrt{3}\)

B is the answer
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shreyaguha005
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Re: Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   12 Aug 2020, 05:35
Carcass wrote:
To have the strip at its maximum height the figure looks like the following

Attachment:
GRE circles.png


The circles are connected at the centers thanks to an equilateral triangle


Attachment:
GRE circles (2).png


H is the following

Attachment:
GRE circles (3).png


so the height is \(h=2\sqrt{3}\)


Adding to this the distances on top and at the bottom of the triangle


Attachment:
GRE circles (4).png


we do have \(4+2\sqrt{3}\)

B is the answer




How can you draw the maximum width without knowing the width? The max width cannot be known and thus the maximum number of circles too can’t be known.
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Re: Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   12 Aug 2020, 05:37
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My apologize

I wanted to say at minimum :)
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Re: Suppose five circles, each 4 inches in diameter, are cut fro [#permalink] New post   20 Sep 2022, 07:58
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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