Hydrostatic forces on a curved surface

Hello,

I'm trying to go through an example problem in a fluid dynamics textbook, and I'm having trouble understanding some of their logic. The problem deals with a solid cylinder of radius 0.8 m hinged at its midpoint that opens when the water it holds back reaches 5 m, and it is asking for the hydro-static forces acting on the cylinder, where the center of the cylinder is 4.2 m below the surface (see attached picture).

Their solution...

For the horizontal force: F_x = F_H = ρgh_cA = (1000 kg/m³) (9.81 m/s²) [4.2 m + (0.8 m/2)] (0.8 m*1 m)

Now, I understand it up until the last part that deals with the area. Firstly, the 1 m length is never mentioned, is this just a typical assumption? Also (probably me missing something very basic here) but what area is radius * length?

For F_y they use the same area component, but when they calculate the weight they use the formula:

W = ρgV = ρg(R² - πR²/4)(1) = (1000 kg/m³) (9.81 m/s²) (0.8 m)² (1-π/4) (1 m)

And again, my question is, what area are they using (multiplied by 1 m) to calculate the volume?

Thanks in advance!

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