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# The interior of a rectangular carton is designed by a

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Manager
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The interior of a rectangular carton is designed by a [#permalink]

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12 Dec 2005, 06:24
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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. 3√x
B. 3√[(2x)/3]
C. 3√[(3x)/2]
D. (2/3) 3√x
E. (3/2) 3√x
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12 Dec 2005, 09:29
C

3L=2H => L=2/3H

2W=2H => H =W

L*H*W = x

2/3H*H*H=x

H^3=3/2x

H=(3/2x)^1/3
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12 Dec 2005, 09:46

Volume = LBH = x
Since L:B:H = 3:2:2, the volume x= 3a.2a.2a

therefore x = 12a^3
or a = (x/12)^(1/3) (i.e. cubeth root of (x/12))
Since Height H= 2a, H= (2x/3)^(1/3) (Cubeth root of (2x/3))
12 Dec 2005, 09:46
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