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Homework Help: Surface Area help

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Imagine you have a rectangular piece of cardboard measuring 3 feet by 4 feet. You know that if you cut a square out of each corner, you can fold the pieces together and tape them together to make an object that looks like a shoe box:http://www.omahamathtutor.com/wp-content/uploads/2012/03/shoebox.png
    What is the outside surface area of this shoe box shape that maximize the volume?

    2. Relevant equations
    2ab + 2bc + 2ac

    3. The attempt at a solution
    Not sure where to start
  2. jcsd
  3. Apr 14, 2012 #2
    V = L*W*H

    Then express the length, width, and height in terms of x after you remove those four squares from the 4 x [STRIKE]12[/STRIKE] 3 rectangle.
    Last edited: Apr 14, 2012
  4. Apr 14, 2012 #3
    Could you show me how to do that?
  5. Apr 14, 2012 #4
    The length is originally 4, then you cut off two segments of length x from both ends of that side, so L = 4 - 2x. Same thing for the width.

    After cutting out the four squares, you have four flaps that fold up; what would be the height of these flaps?
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