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Math Help - please help me!!

  1. #1
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    please help me!!

    Hi can someone help me solve this problem,please!!

    A piece of cardboard measures 40 cm by 40 cm. An open-topped box is to be constructed by removing a square with side length of 8 cm from each corner and folding up the edges.
    a) Find the surface area of the box. b) Find the volume of the box.
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  2. #2
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    Re: please help me!!

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  3. #3
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    Re: please help me!!

    Hello, allison!

    A piece of cardboard measures 40 cm by 40 cm.
    An open-topped box is to be constructed by removing a square with side length of 8 cm
    from each corner and folding up the edges.

    (a) Find the surface area of the box.

    This is simple!

    You start with a 40-by-40 piece of cardboard.
    Its area is: 40\times40 \,=\,1600 \text{ cm}^2.

    You remove four 8-by-8 squares.
    So you remove: 4 \times (8\cdot8) \,=\,256\text{ cm}^2

    So the surface area of the box must be: 1600 - 256 \,=\,1344\text{ cm}^2.




    (b) Find the volume of the box.

    Did you make any sketches?

    Code:
          : - - -  40 - - - - :
        - *---*-----------*---* -
        : |///|           |///| 8
        : *---* - - - - - *---* -
        : |   :           :   | :
        : |   :           :   | :
       40 |   :           :   | 24
        : |   :           :   | :
        : |   :           :   | :
      . : *---* - - - - - *---* -
        : |///|           :///| 8
        - *---*-----------*---* -
          : 8 : -  24 - - : 8 :
    The corner squares are removed
    . . and the sides are folded upward on the dotted lines.


    The open-top box looks like this:

    Code:
              *-----------*
             /|          /|
            / * - - - - / *
           / /         / /
          *-----------* / 24
         8|           |/
          *-----------*
               24
    I assume you can find the volume now . . .

    Last edited by Soroban; September 4th 2012 at 09:27 PM.
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