A cuboid (Rectangular prism has dimension x metres wide, h metres high and 4x metres long. The cuboid is made of 640m of wire.'?

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  • 1 month ago

    You have not asked an actual question. Given the information in your statement, and the length constraint of 640m, we could go on to say, ''Find the dimensions that maximise the volume''

    Length => 4l + 4w + 4h

    so, 4(4x) + 4x + 4h

    Hence, 640 = 20x + 4h

    i.e. h = 160 - 5x

    Now, Volume is lwh => 4x²h

    so, V = 4x²(160 - 5x) => 640x² - 20x³

    Now, dV/dx = 1280x - 60x² = 0 at maximum

    i.e. 20x(64 - 3x) = 0

    Hence, x = 64/3 => 21.33333 metres

    d²V/dx² = 1280 - 120x

    With x = 64/3, d²V/dx² < 0.....confirming maximum

    Then, h = 160 - 5(64/3) => 160/3 metres

    i.e. maximum volume is 4(64/3)²(160 - 5(64/3))

    Hence, 97090m³

    :)>

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  • 1 month ago

    what is the question?

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  • david
    Lv 7
    1 month ago

    wire length  =  4h  +  4L + 4w

       640  =  4h + 4*4x + 4x  >>>  divide by 4

       160  =  h + 5x

    Something is missing ...  Maybe ypu want max volume? or min Vol.?  or max surface area?  or min surface area?  ...  There is nothing else to do unless tthe question asks one of these questions.

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