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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
求NN解答。万分感激！ |
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发表于 2010-8-18 21:13:16
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