Hint: Think of common shapes and how the dimensions differ between different edges!
Manhole covers are quite the elegant design to a commonplace item we interact with on roads every day! The most important problem to solve here, is preventing a manhole cover from falling down the tunnel (imagine a 200 lb. metal disc hurdling down a tunnel).
All manhole covers take the shape of a circle, and at every edge maintains the same diameter. If you were to remove a manhole cover and look at the depths below, you’ll find an inner lip upon which the manhole cover actually sits that has a smaller diameter.
If you were to change to a different shape, take a square for example, you’d start running into fundamental design issues.
To understand this, let’s assume the manhole cover to be square with side length a. The diagonal will be :
Along this length, the cover can then easier fall into the tunnel. A circular shape protects against this length inconsistency because the diameter is the same along all directions.
The cover can easily fall into it along a side. This won’t happen in case of round shape. The diameter is same along all directions.
Other such considerations include that casting a circular shape are inherently simpler in the manufacturing process, and ease of use for workers to re-center the manhole cover over the opening.