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