Posted by Jerry on Wednesday, October 10, 2012 at 11:12am.
Let the center of the tank be at (0,0)
when the water level is at y, the radius of the water surface is
r^2 = 25-y^2
Work is ∫F(y) dy
F(y) is the weight of the water. So, since each slice of water in the tank is raised 21+y feet, and water weighs 62.4 lbs/ft^3,
W(y) = ∫[-5,5] 62.4 π (25-y^2) (21+y) dy
= 218400π
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