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Work necessary to pump gasoline from a tank

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose a large gasoline tank has the shape of a half cylinder 8 feet in diameter and 10 feet long. If the tank is full find the work (W) necessary to pump all the gasoline to the top of ht tank. Assume gasoline wights 42 pounds per cubic foot.


    2. Relevant equations
    W= ∫42(l-x)A(x)dx

    3. The attempt at a solution
    I know i'm suppose to find the crossectional area then which is A(x) and the the height to which i am pumping the oil. But my problem is i cant draw a picture of the problem and i m a visual learner. I tried having the bottom of the tank be at the origin and placing the y axis at the radius of 4. Other than that i not sure where to start. Any help would be appreciated
     
  2. jcsd
  3. Sep 19, 2011 #2

    Mark44

    Staff: Mentor

    Draw a picture of the end view of the tank, which has the shape of the lower half of a semicircle. I would put the origin at the center of the circle, so the the low point of the tank is at (0, -4).

    You don't need a drawing of the whole tank; just the end view will do. The volume of liquid in the tank is the cross-sectional area A(x) times 10.
     
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