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\noindent {\bf Problem statement} 
A right circular
cone has vertex down and is 10 feet tall with base radius 5 feet. The
cone is filled with a fluid having varying density. The density varies
linearly with distance to the top. Here ``varies linearly'' means the
quantities are related by an equation of at most degree 1. At the top
of the cone, the density is 80 lbs/ft$^3$, and at the bottom the
density is 120 lbs/ft$^3$. How much work in ft-lbs is needed to
pump out all the fluid to the top of the cone?

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\noindent Oblique and sideways views of the cone are shown to the
right.}

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