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29 Mar 2018, 00:09
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D
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Difficulty:
45%
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Question Stats:
65% (02:26) correct
35%
(02:25)
wrong
based on 107
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The length, width, and height of a rectangular box are in the ratio of 6:4:5, respectively. Express the height of the box in terms of its volume V.
A. \(\frac{1}{2}*\sqrt[3]{\frac{V}{3}}\)
B. \(\frac{5}{6}*\sqrt[3]{\frac{V}{15}}\)
C. \(2*\sqrt[3]{\frac{V}{15}}\)
D. \(\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
E. \(3*\sqrt[3]{\frac{V}{15}}\)
A. \(\frac{1}{2}*\sqrt[3]{\frac{V}{3}}\)
B. \(\frac{5}{6}*\sqrt[3]{\frac{V}{15}}\)
C. \(2*\sqrt[3]{\frac{V}{15}}\)
D. \(\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
E. \(3*\sqrt[3]{\frac{V}{15}}\)
29 Mar 2018, 01:00
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Bunuel
The length, width, and height of a rectangular box are in the ratio of 6:4:5, respectively. Express the height of the box in terms of its volume V.
A. \(\frac{1}{2}*\sqrt[3]{\frac{V}{3}}\)
B. \(\frac{5}{6}*\sqrt[3]{\frac{V}{15}}\)
C. \(2*\sqrt[3]{\frac{V}{15}}\)
D. \(\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
E. \(3*\sqrt[3]{\frac{V}{15}}\)
A. \(\frac{1}{2}*\sqrt[3]{\frac{V}{3}}\)
B. \(\frac{5}{6}*\sqrt[3]{\frac{V}{15}}\)
C. \(2*\sqrt[3]{\frac{V}{15}}\)
D. \(\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
E. \(3*\sqrt[3]{\frac{V}{15}}\)
As the calculation we're expected to do is straightforward, we'll just do it.
This is a Precise approach.
Writing V for volume and x for the height, we have:
\(V = x *( \frac{x}{5}*4) * (\frac{x}{5}*6) = \frac{24x^3}{25}\)
(Since the width is \(\frac{x}{5}*4\)and the length is \(\frac{x}{5}*6\))
Simplifying gives
\(x = \sqrt[3]{\frac{25V}{24}}=\sqrt[3]{\frac{5^{2}V}{3*2^{3}}}=\sqrt[3]{\frac{5^3V}{5*3*2^3}}=\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
(D) is our answer.
30 Mar 2018, 10:55
Kudos
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Bunuel
The length, width, and height of a rectangular box are in the ratio of 6:4:5, respectively. Express the height of the box in terms of its volume V.
A. \(\frac{1}{2}*\sqrt[3]{\frac{V}{3}}\)
B. \(\frac{5}{6}*\sqrt[3]{\frac{V}{15}}\)
C. \(2*\sqrt[3]{\frac{V}{15}}\)
D. \(\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
E. \(3*\sqrt[3]{\frac{V}{15}}\)
A. \(\frac{1}{2}*\sqrt[3]{\frac{V}{3}}\)
B. \(\frac{5}{6}*\sqrt[3]{\frac{V}{15}}\)
C. \(2*\sqrt[3]{\frac{V}{15}}\)
D. \(\frac{5}{2}*\sqrt[3]{\frac{V}{15}}\)
E. \(3*\sqrt[3]{\frac{V}{15}}\)
We can create the ratio of length : width : height = 6x : 4x : 5x
The volume is 6x * 4x * 5x = 120x^3. So:
120x^3 = V
x^3 = V/120
x = ∛(V/120)
x = ∛(V/(8*15))
x = ∛(⅛) ∛(V/15)
x = ½ ∛(V/15)
Since the height is 5x, height = 5 * ½ ∛(V/15) = 5/2 ∛(V/15).
Answer: D
