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A larger cube has 27 cubic inch as a volume and in the cube there ar

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A larger cube has 27 cubic inch as a volume and in the cube there ar [#permalink]

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New post 15 Jun 2016, 19:56
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Question Stats:

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A larger cube has 27 cubic inch as a volume and in the cube there are 27 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 27 smaller cubes and the surface area of the larger cube, in square inch?
A. 54
B. 64
C. 81
D. 108
E. 120

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[Reveal] Spoiler: OA

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Re: A larger cube has 27 cubic inch as a volume and in the cube there ar [#permalink]

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New post 15 Jun 2016, 20:29
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Volume of larger cube = 27 = 3^3
Side of larger cube = 3

Volume of smaller cube = 1 --> Side of smaller cube = 1

Surface area of larger cube = 6 * 3^2 = 54
Surface area of 27 smaller cubes = 27 * 6 * 1 = 162

Difference = 162 - 54 = 108

Answer: D

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Re: A larger cube has 27 cubic inch as a volume and in the cube there ar [#permalink]

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New post 17 Jun 2016, 02:08
v=volume=a^3=27
therefore, a = 3= side of larger cube
SA larger cube = 6a^2 = 54
p=volume of smaller cube = 1 = z^3=1
therefore , z = 1 =side of the smaller cube
SA smaller cube = 6z^2 = 6
total = 27*6
difference = 27*6-54 = 27(6-2) = 27*4 = 108

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Re: A larger cube has 27 cubic inch as a volume and in the cube there ar [#permalink]

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New post 18 Jun 2016, 00:18
If we calculate 6*27-6*9=108, D becomes our answer.
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Re: A larger cube has 27 cubic inch as a volume and in the cube there ar [#permalink]

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New post 04 Sep 2017, 11:16
I have a small doubt here. But the question says that the volume of the 27 smaller cubes is 1 . so then we need to calculate the volume of one smaller cube right?? Also if we calculate by the above method then the SA of smaller ones are larger than the large cylinder by itself. can this happen ? Kindly explain

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Re: A larger cube has 27 cubic inch as a volume and in the cube there ar   [#permalink] 04 Sep 2017, 11:16
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