Calculus 2: Excercise about "Work Needed"?

I'm not sure if this should be in this thread or in the Physics one, but it was given to me by my Calc2 professor. Thing is, I'm not sure if I'm in the right direction.

"An aquarium measures 2m long, 1m wide and 1m deep and it is full of water. Calculate the work needed to empty it halfway. (Remember that density of water is given by )"

Here's what I have.

Volume ==>

If we want half the volume, then , so the volume I *want* is

Would that make my integral go from 2 to 1? How would I go about the function I'm supposed to integrate?

Thank you!