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

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

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New post 06 Dec 2017, 05:33
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A
B
C
D
E

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  35% (medium)

Question Stats:

76% (02:09) correct 24% (02:39) wrong based on 72 sessions

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

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New post 06 Dec 2017, 05:56
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[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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New post 06 Dec 2017, 05:56
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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Answer is B IMO

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

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New post 06 Dec 2017, 11:16
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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New post 06 Dec 2017, 11:18
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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Answer is B IMO

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

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New post 08 Dec 2017, 13:57
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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Re: A cube with volume 27 is cut into 8 smaller cubes having equal volumes  [#permalink]

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New post 31 Dec 2018, 07:08
1. Using the idea of scale factor, a cube divided into 8 parts has a factor of k^3=8 or k=2.
2. So each side of large cube is twice as big as a small cube (side small = 3/2)
3. Find SA small cube, 6(3/2)^2 = 13.5
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Re: A cube with volume 27 is cut into 8 smaller cubes having equal volumes   [#permalink] 31 Dec 2018, 07:08
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