HMMT 二月 2003 · 冲刺赛 · 第 5 题
HMMT February 2003 — Guts Round — Problem 5
题目详情
- [6] Compute the surface area of a cube inscribed in a sphere of surface area π .
解析
- Compute the surface area of a cube inscribed in a sphere of surface area π . Solution: 2 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.