6. A tank, formed by rotating the curve

around the y-axis, is filled with water, which weighs 62.5 pounds per cubic foot. How much work is done by pumping all the water in the tank to a point 10 foot above the top of the tank?

(In the handout the second factor in x =sqrt(y)*(y-12) should be 12- y.)

The graph of

looks like this:

A typical circular cross section at height y will have volume Pi x² dy,

weight 62.5 Pi x² dy, and will be lifted (22-y) feet. So the work done

will be the integral