Center of Gravity in a Horizontal Cylinder with Water

[chinocr3]

Homework Statement

I need to find the center of gravity of a horizontal cylinder that has water in it, the level of water changes so I need to determine a relation between the diameter occupied by the water and the masses, those are my guesses.

I solved the problem where i have the standing cylinder where the C of G depends of the height of the water.

I added an attachment where you can see the formulas i used.

Homework Equations

How can I make a similar relation with the horizontal cylinder?

The Attempt at a Solution

Maybe using D as the variable instead of h?

m0 = ( (D²∏h)/4 )* ρ

where D² = variable

and ∏h/4 = constant?

sorry if the answer is obvious, I'm really bad at physics $:

 

[SteamKing]

If the cylinder is on its side, try setting up the problem from scratch. I don't think trying to manipulate calculations for a vertical cylinder will be very easy.

 

[CWatters]

I need to find the center of gravity of a horizontal cylinder that has water in it

The horizontal position is obvious so that leaves the vertical position...

You just need to find the center of area of the area under a chord of a circle.