HMMT 二月 2001 · GEN2 赛 · 第 1 题

英文解析

1. A circle of radius 3 crosses the center of a square of side length 2. Find the differencebetween the areas of the nonoverlapping portions of the figures.
   Solution: Call the area of the square s , the area of the circle c , and the area of theoverlapping portion x . The area of the circle not overlapped by the square is c − x and theare of the square not overlapped by the circle is s − x , so the difference between these twois ( c − x ) − ( s − x ) = c − s = 9 π − 4 .2