This question was posed by my grandfather during dinner with him my first night in Key Largo.
The answer to this question can, naturally, be answered using just a little bit of math.
As a table, we collectively came up with two solutions.
1) By using a circular design, the manhole cover can be oriented in any direction, thereby making it easier to place because, being made of cast iron, they aren't particularly light.
2) They can't fall through. If one were to use a polygonal shape, such as a square, where the distance between two opposite points is greater than the length of any one side, then the cover would be able to fall through the hole.
Later, reflecting upon the question further, I came up with another answer using the semantics of geometry where I realized that the shortest path that can be taken where one starts at a single point and finishes at that same point is, in fact, a circle. This solution would allow for the least amount of iron possible to be used in the production of a manhole.
Math is cool :)