And none of this takes into account the restaurant facts, such as that they don't use the whole plate - often food is either piled in the middle and sauces or oils are drizzled around the outside.
Or they use all of the inside of the plate, but none of the RIM - and the Rims can be quiet large too.

Not to mention we're assuming flat round plates - not bowls, and not square or oval or oblong dishes, all of which make a difference.