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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] New post 11 Oct 2005, 14:57
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

Pls show working.....
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 [#permalink] New post 11 Oct 2005, 15:25
B.
I assume you meant :
3√[(2x)/3]
as cube root of (2x/3)

let length, width and hieght are:
3y, 2y, and 2y resp.
V = 12 y^2 = x (given)

or y = (x/12) ^ 1/3 or
2y = (2x/3) ^ 1/3
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 [#permalink] New post 12 Oct 2005, 06:05
OA is B. But if y = (x/12)^1/3 then 2y should be (x/6)^1/3. what am i missing here????
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 [#permalink] New post 12 Oct 2005, 12:10
(3y)(2y)(2y) = 12y^3 = x

y = (x/12)^(1/3)

2y = 2(x/12)^(1/3)

since 8^(1/3) = 2...

8^(1/3) * (x/12)^(1/3) = 2y = height

(8x/12)^(1/3) = (2x/3)^(1/3)

B
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 [#permalink] New post 13 Oct 2005, 06:52
Thanks MsStephanie... that really helped !
  [#permalink] 13 Oct 2005, 06:52
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