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Math Help - Optimization Problem 2

  1. #1
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    Optimization Problem 2

    A cylindrical metal can is made to hold 500 mL of soup. Determine the dimensions of the can that will minimize the amount of metal required. Assume that the top and sides of the can are made from metal of the same thickness.

    I need help with finding the domain of the r value.

    I have

    rE(0, ?]

    How would I find the largest r value? I know that the largest value occurs when h is the smallest. The height.. could it be 0? But then this doesn't make sense:
    V=500
    500=pi r ^2 h
    so if h = 0 then it cancels out r, and I can't find the largest value of r.

    Please help me find the domain of the r value. Thanks
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  2. #2
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    Quote Originally Posted by john-1 View Post
    A cylindrical metal can is made to hold 500 mL of soup. Determine the dimensions of the can that will minimize the amount of metal required. Assume that the top and sides of the can are made from metal of the same thickness.

    I need help with finding the domain of the r value.

    I have

    rE(0, ?]

    How would I find the largest r value? I know that the largest value occurs when h is the smallest. The height.. could it be 0? But then this doesn't make sense:
    V=500
    500=pi r ^2 h
    so if h = 0 then it cancels out r, and I can't find the largest value of r.

    Please help me find the domain of the r value. Thanks
    suffice it to say that r > 0 and h > 0 ... r has to be a finite value since h must be a (+) value also.
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