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HMMT 二月 2001 · GEN2 赛 · 第 1 题

HMMT February 2001 — GEN2 Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. A circle of radius 3 crosses the center of a square of side length 2. Find the difference between the areas of the nonoverlapping portions of the figures.
解析
  1. A circle of radius 3 crosses the center of a square of side length 2. Find the difference between 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 the overlapping portion x . The area of the circle not overlapped by the square is c − x and the are of the square not overlapped by the circle is s − x , so the difference between these two 2 is ( c − x ) − ( s − x ) = c − s = 9 π − 4 .