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geometry-rectangular carton

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geometry-rectangular carton

by sogmat » Sun Dec 21, 2008 3:48 am
The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3 : 2 : 2. In terms of x, which of the following equals the height of the carton, in feet?

A. Cube root x
B. Cube root (2x/3)
C. Cube root (3x/2)
D. 2/3 (Cube root x)
E. 3/2(Cube root x)

oa b[spoiler][/spoiler]
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by agoyal2 » Sun Dec 21, 2008 5:59 am
Hi sogmat,

Please use the spoiler to hide the OA.

The resolution:
The Sides are in the ration on L:W:H = 3:2:2
So, the 3 sides can be assumed to be 3y, 2y, 2y

Volume of the cube
=> 3y*2y*2y = x
=> 12y^3 = x
=> y = CubeRoot(x/12)

Height
=> 2y
=> 2 * CubeRoot(x/12)
=> CubeRoot (8x/12)
=> CubeRoot(2x/3)

So, B is the correct answer
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