Laterally, a manhole is for man only to get through, but the cover of the hole is not expected to fall through, otherwise, the hole shall be named "coverhole" or something...
Geometrically, the best way to prevent a cover from falling through the hole is to design a round cover. In order to hold the cover, there has to be a base to prevent the falling through. if you design a square base, it possible that side of the cover, although shorter than the side of the base, is longer than the diagonal of the base; that will lead to cover dropping through.
oh my god, too much words to explain this. i drew myself a paper, it is straight and clear...
Of any shapes, the shape of round, provide the maximun area with the lest materials -- the beauty of symmetry. Did God designed anything in the shape square? i can not recall...