KöMaL 2014 K431

A circular rubber band of radius 2 cm is placed between two parallel sticks lying on the table. The sticks are moved towards each other until their separation is 2 cm, compressing the rubber ring between them. The resulting figure consists of two semicircles and two parallel line segments. The length of the rubber band doesn't changed. By what factor did the area enclosed by the rubber band change in the ``compression''?