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Emptying a Tank of Beer

  1. Oct 27, 2013 #1

    eumyang

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    So a cousin has asked me for Calculus help, but my Calculus is rusty. She's in Calculus II (of a 3-semester sequence in the US) and is on Work. I decided to make up a problem for her, but I want to make sure I know what I'm doing.

    1. The problem statement, all variables and given/known data
    A cylindrical tank (16 feet high with a radius of 4 feet) is half full of beer that weighs 63 pounds per cubic foot. Find the work requred to pump beer out through a spout in the top of the tank.

    2. Relevant equations
    [itex]W = {\int_a}^b F(x) dx[/itex]

    3. The attempt at a solution
    I just would like to know if I had set up the integral right.

    The volume of a disk of beer would be [itex]\pi \cdot 4^2 \Delta\ y[/itex]
    The weight of a disk of beer would be [itex]63 \cdot 16\pi \Delta y = 1008\pi \Delta y[/itex]
    The distance to move a disk of beer to the top would be [itex]16 - y[/itex]

    [itex]W = {\int_0}^8 1008\pi (16 - y) dy[/itex]
    Is the integral this? Seems too simple. If so, I can take it from here.

    Thanks in advance.
     
  2. jcsd
  3. Oct 27, 2013 #2

    Office_Shredder

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    That looks good to me.
     
  4. Oct 27, 2013 #3

    eumyang

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    Whew! Glad I'm not totally out of it. Thanks.
     
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