You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 11 foot radius. It is 8.5 feet tall and has 7 feet of water in it.

How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the Kool-Aid contaminated water is =63lbsft3

Okay so I did this problem like this....

The area under the Force vs. Distance curve is the energy required in foot*pounds. Simply it is given by

U = W*1.5 + 1/2*W*(8.5-1.5) = W*(1.5 + 1/2*7.0) = W*5.0

Now, the Weight of water is

W = gamma*Volume = gamma*pi*R*2*h= 62.3*pi*11**2*7.0

W = 1.66e5 lbs

So,

U = W*5= 1.66e5*5.0

U = 8.29e5 ft*lbs

This is part of my online hw... and well. It says it's wrong. Where did I go wrong?