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Math Help - Cuboid question.

  1. #1
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    Cuboid question.

    A cuboid has a total surface area of 150cm^2 with a square base x cm.
    Show that the height, h cm, of the cuboid is given by h=(75-x^2)/(2x).
    Express the volume of the cuboid in terms of x.
    Hence determine its maximum volume as x varies.
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    Re: Cuboid question.

    Quote Originally Posted by grooverandshaker View Post
    A cuboid has a total surface area of 150cm^2 with a square base x cm.
    Show that the height, h cm, of the cuboid is given by h=(75-x^2)/(2x).
    Express the volume of the cuboid in terms of x.
    Hence determine its maximum volume as x varies.
    What have you tried?
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    Re: Cuboid question.

    To be completely honest, I have no idea where to start.
    But for the second bit, I think I would do 150cm^2 * (75-x^2)/(2x) to find the volume, maybe??
    And then for the third bit, I'll find the derivative, let it equal 0 to find x and once I find x sub it back into the volume equation.
    I just don't really understand how to do the first bit.
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    Re: Cuboid question.

    Quote Originally Posted by grooverandshaker View Post
    To be completely honest, I have no idea where to start.
    But for the second bit, I think I would do 150cm^2 * (75-x^2)/(2x) to find the volume, maybe??
    And then for the third bit, I'll find the derivative, let it equal 0 to find x and once I find x sub it back into the volume equation.
    I just don't really understand how to do the first bit.
    You have to do question 1 before question 2. How would you evaluate the total surface area of a cuboid?
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    Re: Cuboid question.

    Um, I'm not too sure.
    Would it be 2x^2+4xh ...
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    Re: Cuboid question.

    Quote Originally Posted by grooverandshaker View Post
    Um, I'm not too sure.
    Would it be 2x^2+4xh ...
    Yes. You are told that the total surface area is 150cm^2.

    So that means 2x^2 + 4xh = 150. Solve this for h.
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    Re: Cuboid question.

    Ok so that'll end up being h=(75 - x^2)/2x.
    Do I need to now sub this into something before I can start with the second question?
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    Re: Cuboid question.

    Right, now how would you evaluate the volume of the cuboid?
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    Re: Cuboid question.

    I don't really know...
    The volume of the cuboid would maybe be h*l*w.
    So I spose that would be x^2*h.
    But, I don't think that's right.
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  10. #10
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    Re: Cuboid question.

    Quote Originally Posted by grooverandshaker View Post
    I don't really know...
    The volume of the cuboid would maybe be h*l*w.
    So I spose that would be x^2*h.
    But, I don't think that's right.
    Yes that's right. You have also found that h = (75 - x^2)/(2x). So substitute this in and you have the volume in terms of x.
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