Asked by Quentin

A cylindrical water tank has radius r=1 meter and height 10 meters. Suppose the tank is lying on its side and is filled halfway with water. How much work does it take to pump all the water out the top of the tank? The height is now 2 meters.
Thanks, I'm not really sure how to cut into pieces to find the integral.
Answered by Quentin
Whoops, Assume gravity is 9.8, wrong name
Answered by Steve
Each slice of water is a rectangle. Its length is 10. If the water has depth y, then the width of the rectangle is

√(1 - (1-y)^2) = √(2y-y^2)

Now you have to figure the water's depth (h), and the height to pump each slice of water is 2-y.

So, you have to integrate on y from 0 to h.

I'm sure google will reveal a similar problem.
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