Problem 29E

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis. a If its height is 4 ft and the radius at the top is 4 ft, find the work required to pump the water out of the tank. b After 4000 ftlb of work has been done, what is the depth of the water remaining in the tank?

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