# How do I solve this Calculus Work problem?

A cylindrical water tank has height 8 m and radius 2 m. If the tank is full of water, how much work is required to pump the water to the level of the top of the tank and out of the tank?

I know that work = force X distance and Force = Mass X gravity and that Mass = Density X volume. I know that water density = 1000 kg/m^3 and that the gravitational constant is 9.8 m/sec^2 I just don't know how to use this information to solve this problem. Any help would be appreciated thanks.

## 1 Answer

Align the x axis vertically with respect to the tank. Let x=0 be at the top of the tank and the positive x axis point to the bottom of the tank. Choose an arbitrary slice of the water that is $dx$ thick. What is the volume of this slice? What is the mass? What is the weight? How much work does it take to elevate that slice to the top of the tank? Once you know how much work it takes, sum up all the slices from top to bottom using integration and you are done :).