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The stiffness of a diving board is proportional to the cube

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The stiffness of a diving board is proportional to the cube [#permalink] New post 21 Jun 2017, 13:06
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The stiffness of a diving board is proportional to the cube of its thickness and inversely proportional to the cube of its length. If diving board A is twice as long as diving board B and has 8 times the stiffness of diving board B, what is the ratio of the thickness of diving board A to that of diving board B? (Assume that the diving boards are equal in all respects other than thickness and length.)

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[Reveal] Spoiler: OA
4

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Re: The stiffness of a diving board is proportional to the cube [#permalink] New post 25 Sep 2017, 07:37
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We can translate what is written in formulas as \(s=\frac{t^3}{l^3}\) where s is stiffness, t is thickness and l is length. Then, if board A has 3 times the length and 8 times the stiffness of table B, the formula is rewritten as \(8s=\frac{t^3}{8*l^3}\) so that \(t^3=8s*8l^3\). Thus the ratio between the cubic thickness of the two tables is \(\frac{64sl^3}{sl^3}=64\) but since this is the cubic ratio we have to compute the cubic root to find the ratio between thickness, i.e. \(64^{\frac{1}{3}}=4\)
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Re: The stiffness of a diving board is proportional to the cube [#permalink] New post 29 Nov 2017, 07:45
IlCreatore wrote:
We can translate what is written in formulas as \(s=\frac{t^3}{l^3}\) where s is stiffness, t is thickness and l is length. Then, if board A has 3 times the length and 8 times the stiffness of table B, the formula is rewritten as \(8s=\frac{t^3}{8*l^3}\) so that \(t^3=8s*8l^3\). Thus the ratio between the cubic thickness of the two tables is \(\frac{64sl^3}{sl^3}=64\) but since this is the cubic ratio we have to compute the cubic root to find the ratio between thickness, i.e. \(64^{\frac{1}{3}}=4\)


Can someone explain this to me? I am really struggling with this problem. I understand how you got to S = t^3/l*3, but I don't understand how you got to the next step. How did you end up with 8*l^3 in the denominator?

Thanks in advance.
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Re: The stiffness of a diving board is proportional to the cube [#permalink] New post 29 Nov 2017, 10:01
I believe 6 would be the right answer.
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Re: The stiffness of a diving board is proportional to the cube [#permalink] New post 29 Nov 2017, 12:49
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Please, Guys, refering to the explanation provided by @ilcreatore. it is perfect.

The OA is 4.

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Re: The stiffness of a diving board is proportional to the cube [#permalink] New post 29 Nov 2017, 13:44
The error is the incorrect transcription of the question. The initial question and math is done with the length being twice as great while the forum explanation is 3 times.
Re: The stiffness of a diving board is proportional to the cube   [#permalink] 29 Nov 2017, 13:44
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