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Math Help - Finding Volume of a Box

  1. #1
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    Finding Volume of a Box

    Im a little confused with this problem:




    A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 3 cm squares from each corner and folding up the sides. Let x represent the width of the original piece of cardboard. Find the width of the original piece of cardboard, x, if the volume of the box is 3300 cm squared.

    ---


    I think this is how you set up the equation, but im having trouble factoring it out in the end.. so im not sure if I have it set up right.

    (6)(2x-6)(x-6)= 3300
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  2. #2
    Member rtblue's Avatar
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    Where is the initial 6 coming from?
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  3. #3
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    3+3 to get the height ? am i not supposed to do that with this problem ?
    Last edited by Jerry99; December 4th 2010 at 11:54 AM. Reason: mistake
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  4. #4
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    wait.. i dont know why I did that. Am i supposed to just divide the 3300 by 3?


    so it would be

    (3)(2x-6)(x-6)=3300?
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  5. #5
    Member rtblue's Avatar
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    yes, your reasoning is correct. Now we foil:

    3(x-6)(2x-6)=3300

    3(2x^2-18x+36)=3300

    6x^2-48x+108=3300 Now we divide by 6:

    x^2-9x+18=550

    x^2-9x-532=0

    (x-28)(x+19)=0

    x must be 28, since a negative value is not possible.
    Last edited by rtblue; December 4th 2010 at 02:59 PM.
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  6. #6
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    Hello, Jerry99!

    \text{A piece of cardboard is twice as long as it is wide.}
    \text{It is to be made into a box with an o{p}en top}
    \text{by cutting 3 cm squares from each corner and folding up the sides.}

    \text{Let }x\text{ represent the width of the original piece of cardboard.}

    \text{Find the width of the original piece of cardboard }x,
    \text{if the volume of the box is 3300 cm}^3.

    The cardboard looks like this:

    Code:
          : - - - - 2x- - - - - :
        - *---*-----------*---* -
        : |///:           :///| 3
        : * - *-----------* - * -
        : |   |           |   | :
        x |   |           |   | x-6
        : |   |           |   | :
        : * - *-----------* - | -
        : |///:           :///| 3
        - *---*-----------* - * -
          : 3 : -  2x-6 - : 3 :



    The box looks like this:

    Code:
              *-----------*
             /|          /|
            / * - - - - / *
           / /         / /
          *-----------* / x-6
        3 |           |/
          *-----------*
               2x-6


    The volume is 3300 cm ^3.

    So we have: . 3(2x-6)(x-6) \:=\:3300

    . . which simplfies to: . x^2 - 9x - 532 \:=\:0

    . . which factors: . (x - 28)(x + 19) \:=\:0

    . . and has the positive root: . x \:=\:28\text{ cm.}

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  7. #7
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    thanks for the help guys
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