Pumping a cylindrical tank
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.
I set the bottom of the tank at the point (0,0) & then drew a circle with a radius of 4.
then solved the the circle's equation for x, x=
10-y should be the distance the work must do
Then I distributed the (10-y)
W=22800 - 2280 y
For part two, I set u=16-y^2 & got
W=22800 + 1140 y
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?