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Math Help - barrels, max volume. lowest price

  1. #1
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    barrels, max volume. lowest price

    Ok, so this is a rather interesting problem. Question states:
    An old method to decide the price of a wine barrel was decided like this. You stick a measuring stick from the tap hole S until it touches the the lid D. The lenght SD = d was used to decide the price of the barrel. The astronom kepler said that the best buy of a barrel is if h=2d/ (3)^1/2. without using derivatives.
    And you have this picture of half av the barrel written as h/2 to point s. the hyptenus is the distance d. is kepler right?
    So i want to solve the problem like this. I want to know the maximum volume and the minimum distance d (SD). and im thinking about using the derivative of a cylinder which is 2pi*r^2 * h = volume cylinder. and for swapping out h. So here is where i get stuck. i can use pythagoras theorem for half of the barrel. d^2 = h^2 + r^2. Now the problem is that i end up with two variables no matter what. And i feel that i dont want to use keplers formula since i want to find out the maximum value and compare it to his value.
    All help is appreciated
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Zamzen View Post
    Ok, so this is a rather interesting problem. Question states:
    An old method to decide the price of a wine barrel was decided like this. You stick a measuring stick from the tap hole S until it touches the the lid D. The lenght SD = d was used to decide the price of the barrel. The astronom kepler said that the best buy of a barrel is if h=2d/ (3)^1/2. without using derivatives.
    And you have this picture of half av the barrel written as h/2 to point s. the hyptenus is the distance d. is kepler right?
    So i want to solve the problem like this. I want to know the maximum volume and the minimum distance d (SD). and im thinking about using the derivative of a cylinder which is 2pi*r^2 * h = volume cylinder. and for swapping out h. So here is where i get stuck. i can use pythagoras theorem for half of the barrel. d^2 = h^2 + r^2. Now the problem is that i end up with two variables no matter what. And i feel that i dont want to use keplers formula since i want to find out the maximum value and compare it to his value.
    All help is appreciated
    Please try to make this clearer, so spacing might help as would a diagram

    CB
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  3. #3
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  4. #4
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    thank you.
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