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May 11th, 2011, 01:37 PM   #1
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Smallest area and Smallest Length of String around Box

I have a problem!

I have attached it to this post, just open the attachment please.
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File Type: doc CD1_SolsMan_Ch4.doc (64.0 KB, 30 views)
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May 11th, 2011, 10:38 PM   #2
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Re: Smallest area and Smallest Length of String around Box

Can anyone give me a few pointers????
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May 11th, 2011, 11:34 PM   #3
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Re: Smallest area and Smallest Length of String around Box

We have a rectangular box of a given volume V. The dimensions of the box can be labeled x, y, and z. The volume is then:



The length L of string wrapped around the box (as in your second diagram) is:



Now, if x = y as in your second diagram, we have:

(1)

(2)

Solving (1) for z, we find and substituting for z into z, we get:



Differentiating L with respect to x yields:







Since for x > 0, we know the critical value found gives a minimum. Thus, the dimensions of the box are:

,
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May 12th, 2011, 12:37 AM   #4
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Re: Smallest area and Smallest Length of String around Box

how can i apply this to the first diagram??

Quote:
The first part of the question asks me to find the length of string in terms of width and Volume?
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May 12th, 2011, 12:43 AM   #5
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Re: Smallest area and Smallest Length of String around Box

Sorry, maybe this may make it clearer

Open the following attachment, the diagram is hoppefully clearer...

Thankyou anyone who helps. I really appreciate it!!
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File Type: docx I have a problem.docx (25.0 KB, 24 views)
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May 12th, 2011, 02:37 AM   #6
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Re: Smallest area and Smallest Length of String around Box

can anyone help me please????
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