I'm trying to set the ratio between the variation of the diameter cutting in the region lower a sphere with respect to distance from the center of mass with the center of the radius of the sphere.
For example, if the diameter is zero the center of mass is zero. If the diameter lower is equal to the diameter of the sphere, the Center of mass is $1.875$.
I have this equation, but this is relative to $H$.
Using trigonometry could find this reason. But was thinking to have a answer in terms of integration or derivation.
I wanted to understand how was obtained the above equation. I believe that has been by integration.
Something like this: Equation