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What is the length of a rectangular solid of height 6 that

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What is the length of a rectangular solid of height 6 that [#permalink] New post 26 Aug 2004, 09:09
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What is the length of a rectangular solid of height 6 that is twice as long as it is wide, if its volume is the same as that of a cube with total surface area of 864 square inches?
A) 12
B) 14
C) 24
D) 30
E) 36
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Joined: 31 Dec 1969
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 [#permalink] New post 26 Aug 2004, 09:23
volume of rectangle-Lx2Lx6. Lenght of a side of a square is 6xA^2=864 or A^2=144 so A is 12. The volume of the cube is 1728. Then 12xL^2=12^3 or L=12 so the lenght of the rectangle is 24.
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 [#permalink] New post 26 Aug 2004, 18:54
Anonymous wrote:
volume of rectangle-Lx2Lx6. Lenght of a side of a square is 6xA^2=864 or A^2=144 so A is 12. The volume of the cube is 1728. Then 12xL^2=12^3 or L=12 so the lenght of the rectangle is 24.


good work, the only thing is that a cube is not necessarily considered a square. A rectangular solid in which all edges are of equal length is a cube. However, it doesn't have to have 90 degree angles and thus doesn't have to be a square. Great solution nevertheless
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 [#permalink] New post 27 Aug 2004, 06:25
OA is 24
Just thought 12 could have been a trap answer for someone not paying carefull attention to the "length" instead of the "width"
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  [#permalink] 27 Aug 2004, 06:25
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