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May 11th, 2011, 01:37 PM  #1 
Newbie Joined: May 2011 Posts: 5 Thanks: 0  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. 
May 11th, 2011, 10:38 PM  #2 
Newbie Joined: May 2011 Posts: 5 Thanks: 0  Re: Smallest area and Smallest Length of String around Box
Can anyone give me a few pointers????

May 11th, 2011, 11:34 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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: , 
May 12th, 2011, 12:37 AM  #4  
Newbie Joined: May 2011 Posts: 5 Thanks: 0  Re: Smallest area and Smallest Length of String around Box
how can i apply this to the first diagram?? Quote:
 
May 12th, 2011, 12:43 AM  #5 
Newbie Joined: May 2011 Posts: 5 Thanks: 0  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!! 
May 12th, 2011, 02:37 AM  #6 
Newbie Joined: May 2011 Posts: 5 Thanks: 0  Re: Smallest area and Smallest Length of String around Box
can anyone help me please????


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