HMMT 二月 2001 · 几何 · 第 2 题
HMMT February 2001 — Geometry — Problem 2
题目详情
英文原题
- Call three sides of an opaque cube adjacent if someone can see them all at once. Drawa plane through the centers of each triple of adjacent sides of a cube with edge length 1.
Find the volume of the closed figure bounded by the resulting planes.
解析
英文解析
- Call three sides of an opaque cube adjacent if someone can see them all at once. Drawa plane through the centers of each triple of adjacent sides of a cube with edge length 1.
Find the volume of the closed figure bounded by the resulting planes.
Solution: The volume of the figure is half the volume of the cube (which can be seenby cutting the cube into 8 equal cubes and realizing that the planes cut each of these cubesin half), namely .1 2