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30 Nov 2017, 23:50
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A
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Difficulty:
25%
(medium)
Question Stats:
78% (01:48) correct
22%
(01:58)
wrong
based on 81
sessions
History
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What is the length, in centimeters, of an edge of a cube whose surface area is k square centimeters and whose volume is k/2 cubic centimeters?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36
01 Dec 2017, 10:39
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Bunuel
What is the length, in centimeters, of an edge of a cube whose surface area is k square centimeters and whose volume is k/2 cubic centimeters?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36
Volume of cube =\(\frac{k}{2}\) \(cm^3\)(A) 3
(B) 6
(C) 9
(D) 12
(E) 36
Surface area of cube = \(6s^2 = k\) \(cm^2\)
Surface area to find side in terms of \(k\)
\(6s^2 = k\)
\(s^2 = \frac{k}{6}\)
\(s = \frac{\sqrt{k}}{\sqrt{6}}\)
Volume to find numeric value of \(k\)
Volume =\(\frac{k}{2}\) \(cm^3\)
\((\frac{\sqrt{k}}{\sqrt{6}})^3 = \frac{k}{2}\)
\(\sqrt{k} * \sqrt{k} * \sqrt{k} = k\sqrt{k}\)
\(\sqrt{6} * \sqrt{6} * \sqrt{6} = 6\sqrt{6}\)
\(\frac{k\sqrt{k}}{6\sqrt{6}} = \frac{k}{2}\)
\(2(k)\sqrt{k} = (k)6\sqrt{6}\)
\(\sqrt{k} = 3\sqrt{6}\)
\((\sqrt{k})^2 = (3\sqrt{6})^2\)
\(k = 54\)
Surface area to find side length of cube
Surface area of cube = \(6s^2 = k\) \(cm^2\)
\(6s^2 = 54\)
\(s^2 = 9\)
\(s = 3\) \(cm\)
I think Answer A
01 Dec 2017, 11:46
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Bunuel
What is the length, in centimeters, of an edge of a cube whose surface area is k square centimeters and whose volume is k/2 cubic centimeters?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36
\(6a^2 = k\)
\(a^3 =\frac{k}{2}\)
Lets get a commen power 6
\(6^3 * a^6 = k^3\)
\(a^6 = \frac{k^2}{4}\)
\(6^3 * \frac{k^2}{4} = k^3\)
\(\frac{6^3}{4} = k\)
\(54 = k\)
\(6a^2 = 54\)
\(a^2 = 9 => 3\)
The answer is A
