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HMMT 二月 2003 · 冲刺赛 · 第 5 题

HMMT February 2003 — Guts Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [6] Compute the surface area of a cube inscribed in a sphere of surface area π .
解析

英文解析

  1. Compute the surface area of a cube inscribed in a sphere of surface area π .
    Solution: 2
    The sphere’s radius r satisfies 4 πr = π ⇒ r = 1 / 2, so the cube has body diagonal 1,2
    √ √
    hence side length 1 / 3. So, its surface area is 6(1 / 3) = 2.2