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Homework Help: Use a standard A4 paper to form a block

  1. May 14, 2006 #1
    Hi!
    How to use a A4 paper to form a largerest volume block?
     
  2. jcsd
  3. May 14, 2006 #2

    HallsofIvy

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    I don't believe "A4 Paper" is a standard mathematical term!:wink:
    According to Wikpedia, A4 paper has height to width ratio of [itex]\sqrt{2}:1[/itex].

    Now, are we allowed to cut the paper rather than just folding it? I assume the "block" can be a general rectangular solid, not necessarily a cube.
    If a rectanglar solid has dimensions x, y, z, then it has volume xyz and surface area 2xy+ 2yz+ 2xz. Taking the width of the paper to be 1, the height [itex]\sqrt{2}[/itex] then the area of the paper to be used is [itex]\sqrt{2}[/itex].

    You are to maximize xyz subject to the requirement that [itex]2xy+ 2xz+ 2yz= \sqrt{2}[/itex]. Since there are 3 unknown variables with only one constraint, I would be inclined to use the "Lagrange multiplier" method.
     
  4. May 14, 2006 #3
    thank you
    this is maths project!
     
  5. May 14, 2006 #4
    We have to make a net of the block!
    However i really don't know how to do this project , can you teach me?
     
  6. May 14, 2006 #5
    if i have some difficulties during do the project ,can i ask u?
     
  7. May 15, 2006 #6

    HallsofIvy

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    What do you mean by "make a net of the block"?
     
  8. May 15, 2006 #7
    also need to draw the net of the block
     
  9. May 15, 2006 #8
    actually i don't how to find the vol.
     
  10. May 16, 2006 #9
    Can you simlify the answer?
    I am a form 3 student from HK.,it is really difficult for me to understander the answer.Could you help me?
     
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