HMMT 二月 2003 · GEN1 赛 · 第 5 题
HMMT February 2003 — GEN1 Round — Problem 5
题目详情
英文原题
- A room is built in the shape of the region between two semicircles with the same centerand parallel diameters. The farthest distance between two points with a clear line ofsight is 12 m. What is the area (in m ) of the room?2
解析
英文解析
- A room is built in the shape of the region between two semicircles with the same centerand parallel diameters. The farthest distance between two points with a clear line ofsight is 12 m. What is the area (in m ) of the room?2
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