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# 64 small identical cubes are used to form a large cube

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64 small identical cubes are used to form a large cube [#permalink]  16 Apr 2013, 13:51
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64 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?

A. 64
B. 128
C. 152
D. 216
E. 256
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Apr 2013, 23:28, edited 1 time in total.
Edited the question.
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Re: 64 small identical cubes are used to form a large cube [#permalink]  16 Apr 2013, 13:58
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The side of the cube is N. The area is $$N^3=64$$ so $$N=4$$, there are 4 cubes on each side
To make this cube "one cube longer" we have to add one cube at both ends of a side $$1+4+1=6$$, the new cube will have an area of $$6^3=216$$ cubes.

The difference in the areas will be the number of cubes we've added: $$216-64=152$$

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Re: 64 small identical cubes are used to form a large cube [#permalink]  16 Apr 2013, 23:32
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Expert's post
guerrero25 wrote:
64 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?

A. 64
B. 128
C. 152
D. 216
E. 256

Similar questions to practice:
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html

Hope it helps.
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Re: 64 small identical cubes are used to form a large cube [#permalink]  17 Apr 2013, 04:43
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Another way of solving this

Since the volume is 64 so the side must be 4 units each

The total no. of unit cubes to "coat" the bigger cube would be as

4^2=16 cubes to cover each face so 16*6=96
4 cubes on each edge so 4*12 = 48
one at each corner so 8

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Re: 64 small identical cubes are used to form a large cube [#permalink]  21 Sep 2013, 04:08
aceacharya wrote:
Another way of solving this

Since the volume is 64 so the side must be 4 units each

The total no. of unit cubes to "coat" the bigger cube would be as

4^2=16 cubes to cover each face so 16*6=96
4 cubes on each edge so 4*12 = 48
one at each corner so 8

Hi! I did not understand why you did 4^2, and why 8 more cubes are required at the corners.
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Re: 64 small identical cubes are used to form a large cube [#permalink]  21 Sep 2013, 05:20
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vjns wrote:
aceacharya wrote:
Another way of solving this

Since the volume is 64 so the side must be 4 units each

The total no. of unit cubes to "coat" the bigger cube would be as

4^2=16 cubes to cover each face so 16*6=96
4 cubes on each edge so 4*12 = 48
one at each corner so 8

Hi! I did not understand why you did 4^2, and why 8 more cubes are required at the corners.

The 4^ 2 is because there are 4 cubes on one side of the face. A face has 4 sides ( which makes it a square), so one face has 4+4+4+4 = 16 cubes.
Then, there are 6 faces, so 16*6 = 96 cubes
There are also 4 cubes on each edge = 4*12= 48
and since there are 8 corners in a big cube ( 4 that you can see, 4 at the back, and one at the bottom that you cant see). If you draw a cube and try counting the edges you'll find 8 edges
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Re: 64 small identical cubes are used to form a large cube [#permalink]  20 May 2014, 08:51
64 small cube will make a large cube with 4 cubes in each line i.e.
Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.

Total number of small cubes in new cube = 6^3 = 216

Extra cube required = 216 - 64 = 152

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Re: 64 small identical cubes are used to form a large cube [#permalink]  23 May 2014, 02:07
Smaller cube = 4 x 4 x 4

Larger cube possible = 6 x 6 x 6

Two sides = 6 * 6 * 2 = 72

Remaining 4 sides = 16 * 4 = 64

4 corners = 4 * 4 = 16

Total = 72 + 64 + 16 = 152
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Re: 64 small identical cubes are used to form a large cube   [#permalink] 23 May 2014, 02:07
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