A large conical paper cup has height 1 m. and top radius $\displaystyle \frac{1}{4} m.$ It is filled with water to a height of $\displaystyle \frac{3}{4} m$. Write (but do not evaluate) an integral that equals the work required to empty the cup by pumping all of the water to the top. (Note: The density of water is $\displaystyle 1000kg/m^3$. Answer needs to be in terms of a single variable.

**I'm sure there is a good explanation in a previous thread that I could use. If someone knows of one and can direct me there, that's fine. Or if someone feels like walking me through this, I'd love it! I never really fully understood these work problems.

Thanks