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dP/dR= (density)*w^2*R

Show that the liquid surface is a paraboloidal form; that is a vertical cross section of the surface is the curve y = (w^2*R^2)/2g

MY ATTEMPT:

Since the form of the liquid surface is due to the pressure on the outside of the cylinder, making the liquid level high there. My idea is to find the pressure. So I integrated the variation of pressure given and found:

P = (<density>*w^2*R^2)/2 + C

I try all what possible for me to try to get the y given above but I cant..i dont know how to bring g (the gravitational acceleration)..anybody has any idea???