I am having a hard time with this one.
A horizontal cylinder has D = 2m and L = 4m. The drum is slowly filled with benzene (density =.879 g/cm^3). Derive a formula for the weight of the benzene as a function of the depth (h) of the liquid in centimeter. So basically it wants the wight of the benzine as a function of the height of the liquid as it rises in the drum. I though about using the circle formula in cartesian coordinates and the integrating but I am not sure what the limits would be.
I have (x-1)^1 + y^2 = r^2. This is like the drum is on its side and it is being filled from left to right if you can image it on an xy diagram. The point of filling would be at the origin, cut the circle in half and only take the left hand side of the circle, so you have x= -sqrt(r^2-y^2)-1. Then just divide by 2 to just worry about just the top portion. So you basically have a curve increasing in the x and y direction in the first quadrant. Then multiply by two at the end to get the whole thing. I know that sound very confusing but if someone could at least give me an idea, that would be great.