Heated metal plate
Q. What happens to a metal plate when it's heated? What about if the plate has a hole in the center?
A. When we heat up a metal plate it expands. But what happens to the size of the hole in the center?
Let's start by thinking about a metal plate with no hole. We heat it up and the entire plate expands. The volume of the plate has increased and so the density of the plate has decreased since we have not changed the mass. Everywhere in the plate is uniformly a new, smaller density.
Now imagine we have a cool plate and we cut a circle out of the center. We then place both the plate with the hole and the circle that we cut out in the oven. Both the plate and the circle heat up and expand, lowering their densities. Since the plate and the circle are the same material they are both at the same new, smaller density. Now what happens if we try to put the hot circle back into the hot plate? They should fit together perfectly! We haven't done anything different than when we left the circle in the plate, and in that case nothing funny happened in the center.
So, since we know that the circle expanded to a larger radius then the hole in the center of the plate should also have expanded.