It seems the characterisation of the "lowest energy" state of an iceberg is not correct for all objects For instance, if the iceberg is a long thin cylinder, it is obvious to anyone with experience of floating objects, that it will float with its axis horisontal - whereas a vertical alignment gives a lower center of gravity.
Also, once again it seems the extra credit question is easier than the main puzzle.
With nonuniform density, the center of mass could be as much as 0.9⋅√3 below the surface, though such a cube would surely be crushed by water pressure.
It seems the characterisation of the "lowest energy" state of an iceberg is not correct for all objects For instance, if the iceberg is a long thin cylinder, it is obvious to anyone with experience of floating objects, that it will float with its axis horisontal - whereas a vertical alignment gives a lower center of gravity.
Also, once again it seems the extra credit question is easier than the main puzzle.
With nonuniform density, the center of mass could be as much as 0.9⋅√3 below the surface, though such a cube would surely be crushed by water pressure.