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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42 GPA: 3.82
A larger cube has 27 cubic inch as a volume and in the cube there ar  [#permalink]

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Difficulty:   5% (low)

Question Stats: 93% (01:47) correct 7% (01:58) wrong based on 62 sessions

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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

*An answer will be posted in 2 days.

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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1683
Location: India
Re: A larger cube has 27 cubic inch as a volume and in the cube there ar  [#permalink]

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1
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

Director  G
Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
Re: A larger cube has 27 cubic inch as a volume and in the cube there ar  [#permalink]

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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: A larger cube has 27 cubic inch as a volume and in the cube there ar  [#permalink]

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If we calculate 6*27-6*9=108, D becomes our answer.
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Manager  B
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 186
Location: India
Re: A larger cube has 27 cubic inch as a volume and in the cube there ar  [#permalink]

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