Final answer:
The work required to empty a half-full cylindrical tank by pumping the water 2 meters above the tank involves using calculus to calculate the potential energy change for each water volume element, considering water density, gravitational acceleration, and the volume and height of the tank.
Step-by-step explanation:
The student's question concerns the work required to empty a half-full cylindrical tank by pumping the water to a level 2 m above the top of the tank. To solve this, we would usually use calculus to integrate the work done lifting each infinitesimal volume of water from its initial height to 2 m above the top. However, since no specific dimensions for the tank are given in the question, we cannot provide a numerical answer. Instead, we can explain the general process which involves calculating the potential energy change for each infinitesimal volume element, which equals the work done against gravity. This requires knowing the density of water, the gravitational acceleration, the height the water needs to be lifted, and the volume of the water in the tank.