HMMT 二月 2003 · GEN1 赛 · 第 5 题
HMMT February 2003 — GEN1 Round — Problem 5
题目详情
- A room is built in the shape of the region between two semicircles with the same center and parallel diameters. The farthest distance between two points with a clear line of 2 sight is 12m. What is the area (in m ) of the room?
解析
- A room is built in the shape of the region between two semicircles with the same center and parallel diameters. The farthest distance between two points with a clear line of 2 sight is 12m. What is the area (in m ) of the room? Solution: 18 π The maximal distance is as shown in the figure (next page). Call the radii R and r , 2 2 2 2 2 R > r . Then R − r = 6 by the Pythagorean theorem, so the area is ( π/ 2) · ( R − r ) = 18 π . 1