# Problem K. 431. (October 2014)

**K. 431.** 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''?

(6 pont)

**Deadline expired on November 10, 2014.**

### Statistics:

116 students sent a solution. 6 points: 73 students. 5 points: 13 students. 4 points: 9 students. 3 points: 5 students. 2 points: 3 students. 1 point: 8 students. 0 point: 3 students. Unfair, not evaluated: 2 solutions.

Problems in Mathematics of KöMaL, October 2014