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Math Help - Need help with a basic problem :)

  1. #1
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    Need help with a basic problem :)

    It may be basic, but I'm just going into Calculus now, so I'm kind of hesitant on where to start.

    Question:
    An open box is to be made from cutting squares of side s from each corner of a piece of cardboard 25" by 30"
    a) Write an expressions for the volume, V(s), in terms of s
    b) Draw a graph of V(s)
    c) What domain and range make sense in this problem situation?
    d) Find the value of s that will give the max volume, and what is the max volume?
    e) What value of s will give a volume of 1225 cubic units?

    I just need to know how to start it, because I'm just not sure if I should use surface area, area, or derivative or whatnot.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by glamchic
    It may be basic, but I'm just going into Calculus now, so I'm kind of hesitant on where to start.

    Question:
    An open box is to be made from cutting squares of side s from each corner of a piece of cardboard 25" by 30"
    a) Write an expressions for the volume, V(s), in terms of s
    b) Draw a graph of V(s)
    c) What domain and range make sense in this problem situation?
    d) Find the value of s that will give the max volume, and what is the max volume?
    e) What value of s will give a volume of 1225 cubic units?

    I just need to know how to start it, because I'm just not sure if I should use surface area, area, or derivative or whatnot.
    Start by writing the expression for the volume V in terms of s. The height
    of the box will be s, its length 30-2s, and its depth 25-2s. Drawing a
    picture will also help.

    RonL
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  3. #3
    Super Member

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    Lexington, MA (USA)
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    Hello, glamchic!

    An open box is to be made from cutting squares of side s
    from each corner of a piece of cardboard 25" by 30"
    Some instructions were left out here, right?

    a) Write an expressions for the volume, V(s), in terms of s
    b) Draw a graph of V(s)
    c) What domain and range make sense in this problem situation?
    d) Find the value of s that will give the max volume, and what is the max volume?
    e) What value of s will give a volume of 1225 cubic units?

    I just need to know how to start it, because I'm just not sure if I should use surface area,
    area, or derivative or whatnot.
    Of course you aren't sure . . . you don't understand what it's asking, do you?

    This is the cardboard with the squares to be removed from each corner.
    Code:
          : . . . . 30  . . . :
        - *---+-----------+---*  -
        . |:::|           |:::|  s
        . + - * - - - - - * - +  -
        . |   :           :   |  .
       25 |   :           :   | 25-2s
        . |   :           :   |  .
        . + - * - - - - - * - +  -
        . |:::|           |:::|  s
        - *---+-----------+---*  -
          : s : . 30-2s . : s :

    Then the four "flaps" are folded up to form an open-top box.
    Code:
                *-------------*
              / |           / |
            /   |         /   | s
          *-------------*     |
          |             |     *
        s |             |   /25-2s
          |             | /
          * - - - - - - *
               30-2s

    The volume of a box is: . V\;=\;L \times W \times H

    So we have: . V\;=\;(30-2s_)25-2s)s

    Therefore: . V(s)\;=\;750s - 110s^2 + 4s^3


    Can you continue from here?

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  4. #4
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    Jul 2006
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    Thanks!

    Yess!! Thanks for all your help, you guys! And guess what, I was on the right track! I just doubt myself too much. Thanks again!
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