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Homework Help: Kepler - Wine Barrel Volume

  1. Jun 6, 2007 #1
    1. The problem statement, all variables and given/known data

    A wine barrel has a hole in the middle of its side called a bung hole. To determine the volume of the wine in the barrel, a bung rod is inserted in the hole until it hits the lower seam.
    You should make the following assumptions:
    -The barrel is cylindrical
    -The bung hole is centered along the length of the barrel
    -The distance from the bung hole to the corner is d
    -The ratio of the length to the diameter of the barrel is t.
    Answer the following questions:
    You should show that the volume of the cylindrical barrel is V=2(pi)d^3t(4+t^2)^(-3/2)

    I dont know how to arrive at the fact that the volume would be what is shown.

    2. Relevant equations
    V = pi r^2 h

    3. The attempt at a solution
    I set the two equations next to each other and tried to see what cancelled out which was pi.

    So r ^ 2 h = 2(d^3t)(4+t^2)^(-3/2)

    Then I got stuck and help would be greatly appreciated.
  2. jcsd
  3. Jun 7, 2007 #2


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    Science Advisor
    Homework Helper

    I think you're missing something, since there's no indication anywhere of what [itex]t[/itex] represents.
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