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HMMT 十一月 2009 · 冲刺赛 · 第 4 题

HMMT November 2009 — Guts Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] A cube has side length 1. Find the product of the lengths of the diagonals of this cube (a diagonalis a line between two vertices that is not an edge).
解析

英文解析

  1. [ 6 ] A cube has side length 1. Find the product of the lengths of the diagonals of this cube (a diagonalis a line between two vertices that is not an edge).
    Answer: 576 There are 12 diagonals that go along a face and 4 that go through the center of the
    √ √
    12 4
    cube, so the answer is 2 · 3 = 576.