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Math Help - Solving for volume of rectangular prism

  1. #1
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    Solving for volume of rectangular prism

    If a rectangular prism has faces with areas of 8, 10, and 20 units squared, then what is its volume? The answer is 40. How do I know which side length (length, width, and heighth) corresponds to which given area? Thanks.
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  2. #2
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    Re: Solving for volume of rectangular prism

    Hello, benny92000!

    If a rectangular prism has faces with areas of 8, 10, and 20 units squared,
    then what is its volume? .The answer is 40.

    How do I know which sides (length, width, height) correspond to which given area?

    We don't need that information . . .
    Code:
             *-----------*
            /           /|
           /           / | H
          *-----------*  |
          |           |  *
          |           | /
          |           |/ W
          *-----------*
                L
    We have: . \begin{Bmatrix}LW &=& 8 \\ W\!H &=& 10 \\ LH &=& 20 \end{Bmatrix}

    Multiply the equations: . (LW)(W\!H)(LH) \:=\:(8)(10)(20)

    Hence: . L^2W^2H^2 \:=\:1600 \quad\Rightarrow\quad LW\!H \,=\,40


    Therefore the volume is: . V \:=\:LW\!H \:=\:40\text{ units}^3.

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  3. #3
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    Re: Solving for volume of rectangular prism

    Ok cool. So did you assign LW=8; WH=10; LH=20 arbitarily?
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  4. #4
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    Re: Solving for volume of rectangular prism

    Quote Originally Posted by benny92000 View Post
    Ok cool.
    So did you assign LW=8; WH=10; LH=20 arbitarily?

    Yes, I did.

    Can you see that their assignments made no difference?

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