$($i$)$ Three containers $($Figure a$,$ b$,$ c$)$ have the same bottom shapes but different fluids inside with the same depth. Although the three fluid densities have: ${}_a>{}_b>{}_c,$ but the weight of fluid inside the containers has a relation: Weight of A $.$ Compare the magnitude of hydrostatic force on the bottom for the three scenarios, explain why, and sketch the reaction force exerted on liquid by sidewalls.

$(8$ marks$)$

$($ii$)$ Circular gate ABC is hinged at B$.$ Compute the force just sufficient to keep the gate from opening when h$=8$m$.$ Neglect atmospheric pressure.

$(12$ marks$)$