标题: OG DS一道题目 求解释 [打印本页] 作者: chanxu 时间: 2010-8-18 21:13 标题: OG DS一道题目 求解释 122. What is the volume of a certain rectangular solid? (1) Two adjacent faces of the solid have areas 15 and 24, respectively. (2) Each of two opposite faces of the solid has area 40.
OG解释：(1) If the edge lengths of the rectangular solid are 3, 5, and 8, then two adjacent faces will have areas (3)(5) = 15 and (3)(8) = 24 and the volume of the rectangular solid will be (3)(5)(8) = 120. If the edge lengths of the rectangular solid are 1, 15, 24, then two adjacent faces will have areas (1)(15) = 15 and (1)(24) = 24 and the volume of the rectangular solid will be (1)(15)(24) = 360; NOT suffi cient. (2) If the edge lengths of the rectangular solid are 5, 8, and x, where x is a positive real number, then the rectangular solid will have a pair of opposite faces of area 40, namely the two faces that are 5 by 8. However, the volume is (5)(8)(x), which will vary as x varies; NOT suffi cient. Taking (1) and (2) together, if the edge lengths are denoted by x, y, and z, then xy = 15, xz = 24, and yz = 40, and so (xy)(xz)(yz) = (15)(24)(40), or (xyz)2 = (15)(24)(40). Th us, the volume of the rectangular solid is xyz = (15)(24)(40) . Th erefore, (1) and (2) together are suffi cient. Th e correct answer is C; both statements together are suffi cient.
我的思路：（1）不行 (2)Each of two opposite faces 意思是说每个对面的面积都是40，设dimensions分别为x,y,z.则xy=40;xz=40;yz=40.then (xyz)^2=40*40*40,得到xyz.选B