Underwater symmetry

Consider the above system.The central cube is divided equally into two equal sections. The smaller cubes are attached above and below the central cube such that the centers of all cubes pass through a straight vertical line. The entire system is immersed in water of density pho. The densities of the sections of the central cube and the two smaller cubes is given in the diagram. It was observed that any corner of any cube traced out a quadrant. Given that $l=rs$

If $r$ satisfies the equation $r^a-br-c=0$ , then compute $a+b+c$