hi there,

my question is:

i have a D = {(x,z): ax^2 <= z <= h)}, where a and h are parameters.

if you take this D and rotate it around the z axis,

you get a shape in r^3 - which we'll call V.

we start changing the a parameter, so V changes.

how do i need to change h so that the z coordinate of the center of

mass remains in the same point (the body's mass density is constant)?

i realized that the shape of V is a paraboloid whose outer "radius" is sqrt(h/a) and runs on z from 0 to h. i've tried to calculate a

triple integral of z*dx*dy*dz / the triple integral of 1*dx*dy*dz, but get the answer wrong.

i know my description of the question is somewhat long,

but please help, and thanks in advance...