HMMT 二月 2002 · 冲刺赛 · 第 40 题
HMMT February 2002 — Guts Round — Problem 40
题目详情
- [9] Find the volume of the three-dimensional solid given by the inequality x + y + | z | ≤ 1.
解析
- Find the volume of the three-dimensional solid given by the inequality x + y + | z | ≤ 1. 2 2 Solution: 2 π/ 3 . The solid consists of two cones, one whose base is the circle x + y = 1 in the xy -plane and whose vertex is (0 , 0 , 1), and the other with the same base but vertex (0 , 0 , − 1). Each cone has a base area of π and a height of 1, for a volume of π/ 3, so the answer is 2 π/ 3.