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# A cube with volume 27 is cut into 8 smaller cubes having equal volumes

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Joined: 02 Sep 2009
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A cube with volume 27 is cut into 8 smaller cubes having equal volumes [#permalink]

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06 Dec 2017, 04:33
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71% (01:56) correct 29% (01:25) wrong based on 31 sessions

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A cube with volume 27 is cut into 8 smaller cubes having equal volumes. What is the difference between the surface area of the original cube and the surface area of one of the smaller cubes?

(A) 45.25
(B) 40.5
(C) 27
(D) 24.38
(E) 19
[Reveal] Spoiler: OA

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Kudos [?]: 139595 [0], given: 12794

Intern
Joined: 15 Oct 2017
Posts: 30

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Concentration: Healthcare, Finance
Re: A cube with volume 27 is cut into 8 smaller cubes having equal volumes [#permalink]

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06 Dec 2017, 04:56
[quote="Bunuel"]A cube with volume 27 is cut into 8 smaller cubes having equal volumes. What is the difference between the surface area of the original cube and the surface area of one of the smaller cubes?

(A) 45.25
(B) 40.5
(C) 27
(D) 24.38
(E) 19

Original:
$$a^3 = 27$$
$$a = 3$$
$$6a^2 = 54$$

Cut one:
$$a^3 = \frac{27}{8}$$
$$a = \frac{3}{2}$$
$$6a^2 = 13.5$$

$$54 - 13.5 = 40.5$$ (B is the answer)

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Re: A cube with volume 27 is cut into 8 smaller cubes having equal volumes [#permalink]

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06 Dec 2017, 04:56
Bunuel wrote:
A cube with volume 27 is cut into 8 smaller cubes having equal volumes. What is the difference between the surface area of the original cube and the surface area of one of the smaller cubes?

(A) 45.25
(B) 40.5
(C) 27
(D) 24.38
(E) 19

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Re: A cube with volume 27 is cut into 8 smaller cubes having equal volumes [#permalink]

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06 Dec 2017, 10:16
Bigger cube has each side measuring 3, SA is 54. Smaller will have each side measuring half of the bigger cube, 1.5. SA of smaller cube is 13.5. So the answer is B, 40.5

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Re: A cube with volume 27 is cut into 8 smaller cubes having equal volumes [#permalink]

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06 Dec 2017, 10:18
lesner19 wrote:
Bunuel wrote:
A cube with volume 27 is cut into 8 smaller cubes having equal volumes. What is the difference between the surface area of the original cube and the surface area of one of the smaller cubes?

(A) 45.25
(B) 40.5
(C) 27
(D) 24.38
(E) 19

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A cube with volume 27 is cut into 8 smaller cubes having equal volumes [#permalink]

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08 Dec 2017, 12:57
Whenever a cube is divided into 8 parts, the ratio of side original: small is 2:1.

Now, as side of original cube is 3, side of small cube must be 1.5.

Difference in SA= (6*3^2)-(6*1.5^2)= 6(9-2.25)= 6*6.75= 6*(6+0.75)= 36+(6*3/4)= 36+4.5= 40.5

Ans B

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A cube with volume 27 is cut into 8 smaller cubes having equal volumes   [#permalink] 08 Dec 2017, 12:57
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