KöMaL 2017 K534

Kate has a round table, it is a circle of area 4 m${}^{2}$. She also has a circular tablecloth of exactly the same size to go with it. Joe has a square table, two metres on a side, and a square tablecloth of the very same size. One day, the two of them switched the tablecloths. Each of them laid the other's tablecloth on their own table, with the centre of the cloth carefully positioned on the centre of the table. Each observed that the tablecloth overhung the edge of the table at some places, while the table remained partly uncovered. In which case was the area of the uncovered part greater?