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Math Help - finding volume with algebra

  1. #1
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    Smile finding volume with algebra

    Please help me with this question.

    PUZZLING PRISM:
    The areas of three faces of a rectangular prism are 63 cm2, 56 cm2 and 72 cm2. What is the volume of the prism?

    What I know:

    Volume= LxWxH
    Area = LxW


    Ps. reply asap. thank you very much for your help and your time!
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  2. #2
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    Quote Originally Posted by puppy_wish View Post
    Please help me with this question.

    PUZZLING PRISM:
    The areas of three faces of a rectangular prism are 63 cm2, 56 cm2 and 72 cm2. What is the volume of the prism?

    What I know:

    Volume= LxWxH
    Area = LxW


    Ps. reply asap. thank you very much for your help and your time!
    You know that,
    xy=63
    xz=56
    yz=72
    Multiply them together,
    xyxzyz=63\cdot 56\cdot 72=254016
    x^2y^2z^2=(xyz)^2=V^2=254016
    Thus,
    V=\sqrt{254016}=504
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  3. #3
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    Hello, puppy_wish!

    This can be solved with "normal" algebra
    . . but there is a cute solution . . .


    The areas of three faces of a rectangular prism are 63 cm², 56 cm² and 72 cm².
    What is the volume of the prism?

    Let the length, width, height be: L,\,W,\,H.

    We are told that: . \begin{array}{ccc} LW \,=\,63 \\ WH\,=\,56 \\ LW\,=\,72\end{array}

    Multiply the three equations: . (LW)(WH)(LH) \:=\:(63)(56)(72)

    and we have: . L^2W^2H^2 \:=\:254,016\quad\Rightarrow\quad(LWH)^2\:=\:254,0  16

    Therefore: . LWH \:=\:\sqrt{254,016} \:=\:504\text{ cm}^2


    I like this solution . . . I hope you do.
    We answered the questi0on without finding L,\,W and H.

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, puppy_wish!

    This can be solved with "normal" algebra
    . . but there is a cute solution . . .



    Let the length, width, height be: L,\,W,\,H.

    We are told that: . \begin{array}{ccc} LW \,=\,63 \\ WH\,=\,56 \\ LW\,=\,72\end{array}

    Multiply the three equations: . 63)(56)(72)" alt="(LW)(WH)(LH) \:=\63)(56)(72)" />

    and we have: . L^2W^2H^2 \:=\:254,016\quad\Rightarrow\quad(LWH)^2\:=\:254,0  16

    Therefore: . LWH \:=\:\sqrt{254,016} \:=\:504\text{ cm}^2


    I like this solution . . . I hope you do.
    We answered the questi0on without finding L,\,W and H.

    wow thank you both of you. I really appreciate it
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