A right circular cone that has altitude \(h\) and a base of radius \(R\) is submerged in a liquid of mass density \(ho\). The cone's vertex points directly downward, so that the circular top face of the cone is horizontal. The volume of a right circular cone is \(\pi R^{2} b / 3\).

(a) By direct integration of the pressure over the surface of the cone, calculate the magnitude of the upward force exerted by the liquid on the cone.

(b) Show that your answer in part \(a\) is consistent with Archimedes' principle.