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Math Help - tricky math math question

  1. #1
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    tricky math math question

    thanks for those who try and work on it
    Take a piece of cardboard measuring 7 by 15 inches. Cut congruent squares out of each corner of the cardboard and fold up the edges to form an opened-top box. What is the maximum volume of a box that you can create in this manner?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by anime_mania View Post
    thanks for those who try and work on it
    Take a piece of cardboard measuring 7 by 15 inches. Cut congruent squares out of each corner of the cardboard and fold up the edges to form an opened-top box. What is the maximum volume of a box that you can create in this manner?
    I'll start you off.

    obviously, this is an optimization problem in which we'd like to maximize the volume of a box. so the question is, what formula will give us the volume of the box for us to maximize? let's take this step by step

    did you draw a diagram? (for related rates and optimization problems, ALWAYS draw a diagram if applicable--here, of course, it's applicable)

    Let the side-length of the squares we cut out at each corner be x

    then we have what you see in the diagram below.

    we know that the volume of the box will be given by:

    V = \mbox{length} \times \mbox{width} \times \mbox{height}

    can you tell the length, width and height of the box from the diagram? if you can, there's your formula to maximize!
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