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

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Math Expert
Joined: 02 Sep 2009
Posts: 50078
What is the length, in centimeters, of an edge of a cube whose surface  [#permalink]

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30 Nov 2017, 23:50
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Difficulty:

35% (medium)

Question Stats:

80% (01:49) correct 20% (01:45) wrong based on 21 sessions

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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

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

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01 Dec 2017, 10:39
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 = $$6s^2 = k$$ $$cm^2$$

$$6s^2 = 54$$

$$s^2 = 9$$

$$s = 3$$ $$cm$$

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

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01 Dec 2017, 11:46
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

$$6^3 * a^6 = k^3$$
$$a^6 = \frac{k^2}{4}$$
$$6^3 * \frac{k^2}{4} = k^3$$
$$\frac{6^3}{4} = k$$
$$54 = k$$
$$6a^2 = 54$$
$$a^2 = 9 => 3$$

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

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01 Dec 2017, 12:09
2
1
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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