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Note: Be careful of units, and be sure to look up conversion factors, as needed....

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Accounting

Note: Be careful of units, and be sure to look up conversion factors, as needed.
A water tank is made in the shape of an ellipse, with height 30 feet and width 25 feet, rotated about its central axis. Recall that the equation of an ellipse centered at the origin is x2a2+y2b2=1 where a is the radius in the x direction and b is the radius in the y direction. Assuming the tank is half full, find the work done to pump all of the water out over the top of the tank and into a tanker truck, 10 feet above the tank.
(a) Explain what is wrong with the following solution to the problem.
Work =( Force )*( Distance )=( Total weight of water )**(15ft)
(b) With the origin at the center and the y-axis running vertically through the center of the tank, consider one "slice" of water at level y and with thickness dy. Draw the slice and calculate the amount of work done to lift this "slice" of water up to the tanker.
(c) Set up and evaluate an integral to calculate the total amount of work done to pump all of the water over the top of the tank.
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