Calculus II: Work Problem - Find Work in Pumping Water to Top of Tank

[paiway]

"Work" (Calculus II)

This is a problem from the chapter called "Work":

A water tank in the form of an inverted right-circular cone is 29 ft across the top and 15 ft deep. If the surface of the water is 5 ft. below the top tank, find the work done in pumping the water to the top of the tank. Assume water weights W lbs. per cubic feet (which means your answer will be expressed in terms of W)


I have read it many times but I don't know what to do to solve it...please help, I really appreciate it.

 

[Dick]

Work is weight times distance. At a given distance h below the top of the tank take a slice of the water of thickness dh. The weight is volume of the slice times W. The work to pump it to the top is h*(volume of the slice)*W. Now you need to integrate that over the range of h that includes all of the water in the tank. Is that enough to get started? It's a lot like finding the volume but with those extra factors of W and h.

 

[paiway]

thank you very much...i'm going to see if I can solve it using this :)