HMMT 二月 2003 · 几何 · 第 3 题
HMMT February 2003 — Geometry — Problem 3
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? 2 2
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. Call the radii R and r , R > r . Then 2 2 2 2 2 R − r = 6 by the Pythagorean theorem, so the area is ( π/ 2) · ( R − r ) = 18 π . 2 2