HMMT 二月 2002 · 冲刺赛 · 第 40 题

英文解析

40. 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 theanswer is 2 π/ 3.