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Math Help - box with a lid

  1. #1
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    box with a lid

    Hello
    I need to construct a box with a seamless flap lid that extends down the front to the bottom, (sorta like a pizza box) from a single piece of paper 18x20 that maximizes volume. I solved the open box max volume problem but having a lot of trouble with this one. Can anyone help or show me where to look? Thank you!
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  2. #2
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    more details please...

    I'm not quite sure what you are asking?

    It is just a rectangular prism of any dimensions, as long as the surface area = 18x20?
    I am not sure if there are any parts of the box that overlap.

    EDIT: Squares/Cubes are are always better for maximizing area/volume. So if there are no restricions on the boxes dimensions it would be a cube. If the height is restricted (so it is short like a pizza box) then it would have that height, with a square base.
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  3. #3
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    Thanks for replying

    Ok we are given a sheet of paper 18x20. From that I need to design a box maximixing the volume which is very similair to a pizza box. The clam shell bottom piece has a bottom and three sides, the top has the same 3sides and a top, and finally they are connected using another side forming the back side. So this box overall will have 9 surfaces because the top and bottom fold clam shell over one another. THanks so much!
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  4. #4
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    Hello, jkupcha!

    I have another question . . .


    I need to construct a box with a seamless flap lid that extends down the front to the bottom,
    (sort of like a pizza box) from a single piece of paper 1820 that maximizes volume.

    Can the seven panels be cut separately from the 1820 paper?

    Or does the box need to be folded from a single (strangely shaped) piece?

    (I don't know what "seamless flap" means in this context.)

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  5. #5
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    Hello, jkupcha!

    I don't agree with your description . . .


    We are given a sheet of paper 18x20.
    From that I need to design a box maximixing the volume which is very similair to a pizza box.
    The clamshell bottom piece has a bottom and three sides,
    the top has the same 3 sides and a top, . ... I don't agree
    and finally they are connected using another side forming the back side.
    So this box overall will have 9 surfaces because the top and bottom fold
    clam-shell over one another.
    Are you sure of that?
    Can you give us the wording of the original problem . . . or a diagram?

    From your original post, I assumed the box looked like this:


    Code:
                *-------*
               /       / \
              /       /   \
             /       /     \ 
            *-------*       \
                     \       \
              *-------\       \
             /|        \     /|
            / |         \   / |
           /  |          \ /  |
          *---------------*   *
          |               |  /
          |               | /
          |               |/
          *---------------*
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