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Math Help - The shape of a can

  1. #1
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    The shape of a can

    1. The problem statement, all variables and given/known data

    How do I show that when I have C = 4√(3)r^2 + 2π(r)h + k(4π(r) + h), the cost C to make a cylinder of constant radius V gives the following defining equation: (∛(V))/k = (∛(π(h)/r)) x (2π - h/r)/π(h/r) - 4√(3)

    k is the reciprocal of the length that can be joined for the cost of one unit area of metal.

    2. Relevant equations

    ((h/r) = 8/π ≈ 2.55 is the minimized amount of metal used

    3. The attempt at a solution

    I've tried substituting h = 1000/(πr^2) and then found the derivative with respect to r but it doesn't prove the equation above.
    We haven't learn partial derivatives yet, so is there any other way to solve this?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Hydra911 View Post
    1. The problem statement, all variables and given/known data

    How do I show that when I have C = 4√(3)r^2 + 2π(r)h + k(4π(r) + h), the cost C to make a cylinder of constant radius V gives the following defining equation: (∛(V))/k = (∛(π(h)/r)) x (2π - h/r)/π(h/r) - 4√(3)

    k is the reciprocal of the length that can be joined for the cost of one unit area of metal.

    2. Relevant equations

    ((h/r) = 8/π ≈ 2.55 is the minimized amount of metal used

    3. The attempt at a solution

    I've tried substituting h = 1000/(πr^2) and then found the derivative with respect to r but it doesn't prove the equation above.
    We haven't learn partial derivatives yet, so is there any other way to solve this?
    Post the full question please

    CB
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