The vertical hydrostatic force acting on the dam as shown in Figure Q$.1$ is not to exceed $3\mathrm{.}0$ MN $.$ The curved surface of the dam has a shape prescribed by the relation $y=x^2.$ If the width of the dam is $10$ m $,$ determine:

Figure Q$\mathrm{.}1.$ Schematic of the proposed dam.

i$)$ the height $($ h $)$ of the dam, and

ii$)$ the resultant hydrostatic pressure force acting on the curved surface.

Take density of water as $1000k\frac{g}{m^3}$

$(4+6)$