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6. Choose only one of the following; only the first problem completed will be graded. A 500kg wrecking ball hangs from a 12m long cable of density 15kg/m attached to a winch at the end of a crane. Compute the work required to raise the ball 8m. OR Compute the work required to empty a semi-spherical bowl of radius 2m if it is filled with water. Assume the water is being removed from the top of the bowl. OR Compute the center of mass of a flat plate of sheet metal whose shape is given by the region bound by y = ex, y = x , x = 1, and x = 6. OR Compute the (hydrostatic) force on the ends of an oil drum that is laying horizontally at the bottom of a lake that is 100m deep if the drum has circular ends that are Im in diameter. OR Compute the volume and surface area of the solid obtained by rotating the area enclosed by the graphs of f (x) = =x + 4 and g(x) = x2 - x + 3 about the line x = 4