Set up an integral to compute the work required to empty a conical tank of water

Question

Set up an integral to compute the work required to empty a conical tank of water, assuming the top of the tank is a circular disc of radius 5 meters, and that the tank is 10 meters tall. Assume also that the density of water is 1000 kg/m^3 and that the water exits through a small hole at the top. Solution: Let y be the distance a layer of water in the tank must be lifted to the top; then 10 - y is the distance of the layer to the bottom of the tank. By similar triangles, the radius r(y) of the layer of water at depth y satisfies r(y)/(10 - y) = 5/10 = 1/2. So r(y) = (10 - y)/2. The volume of a thin layer of water at depth y is therefore is the mass of water in the layer. The work required to raise this mass to the top of the tank is Therefore the total work required is represented by

Explanation / Answer

You should better try this yourself. Its a much easier problem

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