I'm Having a similar Problem for a conic
Assume constant density, then mass = volume
I'm looking for the center of gravity
So I assume this means point of equal volume
Let Cone lie on side, let theta = @ ; then Tan@ = radius/height
CONE: V = 1/3 x R^2 x H ; A = pi x R^2 ; R = H x Tan@
Centroid of cone?
cone v = 1/3 x r^2 x h ; A = pi x r^2 ; r = h x Tan@
2 x v = V ???
Then 2/3 x pi x (Tan@)^2 x h^3 = 1/3 x pi x (Tan@)^2 x H^3
therefore 2 x h^3 = H^3 h = 2^(1/3) x H
One/cuberoot of 3 = 0.7937... does not equal 3/4 x H
What is wrong with my logic?????