A cube of side length 2 m is composed of two materials, separated by a plane slanting down from the top corner to cut the bottom face in a diagonal, as in the figure shown below. The material below the plane has density P gm/m3 and the material above the plane has density Q gm/m3. (a) Find the mass of the portion of the cube below the slanted plane. Your answer will be in terms of P. This is an upper case P.
(b) Find the mass of the portion of the cube above the slanted plane. Your answer will be in terms of Q.