Question

If a metal piece with circular hole is heated then diameter increases why?

Answer 1

Many of us "expect" that diameter of hole will decrease, because plate is free to expand in that direction as well. Note that expansion of metal due to heating is not like gas spreading out wherever space is available.

Correct way to think about it is following. Hole size is irrelevant in this case. So we can think that hole is very large. If we carve hole so large such that it's radius is slightly less than that of plate itself, then we will have a ring. It is obvious that radius of ring will increase, as atoms have more energy so there oscillation amplitude will increase. As diameter of ring increases, diameter of hole will also increase.