I found that the solution for a=R is:
V = 2/3*R^2*b
c = R-3/16*PI*R
Hello from Finland!
I have a problem how to calculate the volume and the mass centroid of a partial cylinder. Please look at the image below. I have listed the given information there. Variable for a is: a=0...2R
Ive tried to solve it, but I dont know how to do it... All help is appreciated! Thanks!
Definitions and Orrientation:
I set it up so that:
1) The y-axis is parallel to the cut.
2) The x-axis is the perpendicular bisector of the cut.
3) The z-axis is parallel to 'b'.
4) The entire structure is in the four quadrants were z > 0.
5) The Origin of the x-y plane is at the center of the circle from the top view.
This has two side effects.
1) The centroid for the y-axis is obviously zero (0), due to symmetry.
2) The equation of the cut-plane is (z-0) = (-b/a)(x-R)
3) The centroid for the x-axis should be < 0. Intuitively clear.
The volume, then, would be:
Let's see if you can get that far or if we need a different kind of solution.