PUMaC 2019 · 几何（B 组） · 第 2 题
PUMaC 2019 — Geometry (Division B) — Problem 2
题目详情
- A right cone in xyz -space has its apex at (0 , 0 , 0), and the endpoints of a diameter on its base are (12 , 13 , − 9) and (12 , − 5 , 15). The volume of the cone can be expressed as aπ . What is a ?
解析
- A right cone in xyz -space has its apex at (0 , 0 , 0), and the endpoints of a diameter on its base are (12 , 13 , − 9) and (12 , − 5 , 15). The volume of the cone can be expressed as aπ . What is a ? Proposed by Nathan Bergman and Jacob Wachsprass. Answer: 975 Solution: The center of the base is the midpoint of the diameter (12 , 4 , 3). Then the height of the cone is 13 and the radius of the cone is 15, so the volume is 975 π .