A storage tank is a right circular cylinder 20ft long and 8 ft in diameter with its axis horizontal. If the tank is half full of olive oil weighing 57 lb/ft^3, find the work done in emptying it through a pipe that runs from the bottom of the tank to an outlet that is 6 ft above the top of the tank.

...

This is the part where I get lost, I did it a bit differently from the solutions manual, but at this point the manual shows inserting 4

as follows

22800(4

)+ 1140

y

(evaluated from 0 to -4), I tried from (0 to 4) in my solution.

I don't understand why the solutions manual is doing this particular step, it says its the area of a semicircle, but can anyone explain why I use it in this problem & where the integral disappears to?