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cubned ical box

by treker » Tue Jul 26, 2011 9:51 am
The interiors of a cubical box are designed to hold a volume of V ml. If the length, breadth, and height are in ratio 5:1:3, in terms of V which of the following equals the height of the box in cm?
(1 ml = 1 cm^3)

A. cube root(V) B. 3/cube root(3/V) C. cube root(V/15) D. 3/cube root(15/V) E. 9/(5*cube root(15/V))
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by Anurag@Gurome » Tue Jul 26, 2011 9:39 pm
treker wrote:The interiors of a cubical box are designed to hold a volume of V ml. If the length, breadth, and height are in ratio 5:1:3, in terms of V which of the following equals the height of the box in cm?
(1 ml = 1 cm^3)

A. cube root(V) B. 3/cube root(3/V) C. cube root(V/15) D. 3/cube root(15/V) E. 9/(5*cube root(15/V))
Length: Width : Height = 5 : 1 : 3
Let us assume that Length = 5x, Width = x, and Height = 3x
Then, V = (5x)(x)(3x) implies V = 15(x^3)
x^3 = V/15 or x = cube root(V/15)
Hence, height = 3 * x = 3 * cube root(V/15) = 3/cube root(15/V)

The correct answer is D.
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by treker » Wed Jul 27, 2011 7:15 am
Anurag@Gurome wrote:
treker wrote:The interiors of a cubical box are designed to hold a volume of V ml. If the length, breadth, and height are in ratio 5:1:3, in terms of V which of the following equals the height of the box in cm?
(1 ml = 1 cm^3)

A. cube root(V) B. 3/cube root(3/V) C. cube root(V/15) D. 3/cube root(15/V) E. 9/(5*cube root(15/V))
Length: Width : Height = 5 : 1 : 3
Let us assume that Length = 5x, Width = x, and Height = 3x
Then, V = (5x)(x)(3x) implies V = 15(x^3)
x^3 = V/15 or x = cube root(V/15)
Hence, height = 3 * x = 3 * cube root(V/15) = 3/cube root(15/V)

The correct answer is D.
Thanks much Anurag, but could you please explain how 3 * cube root(V/15) becomes 3/cube root(15/V)?
Thanks!
- Treker

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by Anurag@Gurome » Wed Jul 27, 2011 6:55 pm
treker wrote:
Anurag@Gurome wrote:
treker wrote:The interiors of a cubical box are designed to hold a volume of V ml. If the length, breadth, and height are in ratio 5:1:3, in terms of V which of the following equals the height of the box in cm?
(1 ml = 1 cm^3)

A. cube root(V) B. 3/cube root(3/V) C. cube root(V/15) D. 3/cube root(15/V) E. 9/(5*cube root(15/V))
Length: Width : Height = 5 : 1 : 3
Let us assume that Length = 5x, Width = x, and Height = 3x
Then, V = (5x)(x)(3x) implies V = 15(x^3)
x^3 = V/15 or x = cube root(V/15)
Hence, height = 3 * x = 3 * cube root(V/15) = 3/cube root(15/V)

The correct answer is D.
Thanks much Anurag, but could you please explain how 3 * cube root(V/15) becomes 3/cube root(15/V)?
If you check the given options, there is no option given as 3 * cube root(V/15). And, 3 * cube root(V/15) is one and the same thing as 3/cube root(15/V). So, we chose D as the answer. See this example:
(2/5) ÷ 4 = (2/5) * (1/4) = 1/10
Similarly, 3 ÷ cube root(15/V) = 3 * cube root(V/15)
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