A cylindrical vessel of radius r is filled with a homogenous liquid to a height h. If the force exerted by the liquid on the side of the vessel is equal to the force exerted by it at the bottom of the vessel, then

Force exerted by the liquid at the bottom of vessel isFbottom=(πr2)(hρg)Average pressure exerted on the wall isPav=0+hρg2=12hρgForce exerted on the curved surface of the vessel of area 2πrh isFwall=Pav(2πrh)⇒  Fwall=Pav(hρg)(πrh)Since, both forces are equal, so we geth=r