A $2-$kN$-$cylindrical gate $($with radius r $)$ is connected to a vertical wall by a hinge at A$.$ What is the specific gravity of the unknown fluid to hold the gate in place, if the liquid surface is $\frac{r}{2}$ below the center of the gate?

Area of a sector of a circle $=\frac{1}{2}{r}^2,$ in radians; $1.$Draw and annotates figures that are necessary for this solution; $2.$Write a short narrative of crucial steps, important assumptions made, and all pertinent details that reflects the process.