PUMaC 2010 · 几何（B 组） · 第 7 题
PUMaC 2010 — Geometry (Division B) — Problem 7
题目详情
- A cuboctahedron is a solid with 6 square faces and 8 equilateral triangle faces, with each edge adjacent to both a square and a triangle (see picture). Suppose the ratio of the volume of an 2 octahedron to a cuboctahedron with the same side length is r . Find 100 r .
解析
- A cuboctahedron is a solid with 6 square faces and 8 equilateral triangle faces, with each edge adjacent to both a square and a triangle (see picture). Suppose the ratio of the volume of an 2 octahedron to a cuboctahedron with the same side length is r . Find 100 r . [Answer] 4 [Solution] A cuboctahedron is obtained by chopping off 8 corner tetrahedra of a cube. So √ √ 3 1 2 5 3 volume of cuboctahedron of side length 1 is ( 2) − 8 × (1 / = 2. On the other hand,