A solid cube is $0\mathrm{.}10$ m on an edge. This cube is floating in a lake with one$-$third of its height beneath the surface. $($a$)$ What is the buoyant force acting on the cube? $($b$)$ What is the mass of the cube? $($c$)$ What is the density of the cube? $($d$)$ The cube is then placed in an unknown liquid where $50\mathrm{.}0\%$ of the cube is submerged. Find the density of the unknown liquid.