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What is the length, in centimeters, of an edge of a cube whose surface

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What is the length, in centimeters, of an edge of a cube whose surface [#permalink]

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New post 30 Nov 2017, 22:50
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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
[Reveal] Spoiler: OA

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Re: What is the length, in centimeters, of an edge of a cube whose surface [#permalink]

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New post 01 Dec 2017, 09:39
Bunuel wrote:
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 =\(\frac{k}{2}\) \(cm^3\)
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

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Re: What is the length, in centimeters, of an edge of a cube whose surface [#permalink]

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New post 01 Dec 2017, 10:46
Bunuel wrote:
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


\(6a^2 = k\)
\(a^3 =\frac{k}{2}\)

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

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What is the length, in centimeters, of an edge of a cube whose surface [#permalink]

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New post 01 Dec 2017, 11:09
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KUDOS
Formula used:
Surface area of cube - \(6*a^2\) | Volume of a cube - \(a^3\) where a is the edge of the cube

We are given that
\(6*a^2 = k => a^2 = \frac{k}{6}\) -> (1)
Similarly, \(a^3 = \frac{k}{2}\)

This can be further simplified as \(a^2*a = \frac{k}{2} => a*\frac{k}{6} = \frac{k}{2}\) from (1)

Hence \(a=3\)
Therefore, the length of a cube is 3(Option A)

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Kudos [?]: 750 [2], given: 20

What is the length, in centimeters, of an edge of a cube whose surface   [#permalink] 01 Dec 2017, 11:09
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