A cube that is $5\mathrm{.}0$ cmcm on a side is made from a material with a density of $800$ kg$/$m$3$kg$/$m$3.$ The cube floats in a fluid that has a density of $1200$ kg$/$m$3$kg$/$m$3.$ How much of the height of the cube is underneath the surface of the water?

$1\mathrm{.}7$ cmcm$0\mathrm{.}83$ cmcm$3\mathrm{.}3$ cmcm$4\mathrm{.}2$ cmcm$2\mathrm{.}5$ cmcm