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

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16 Apr 2013, 14:51

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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 ?

Re: 64 small identical cubes are used to form a large cube [#permalink]

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16 Apr 2013, 14:58

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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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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 ?

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21 Sep 2013, 06:20

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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

All add up to 96+48+8=152

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]

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20 May 2014, 09:51

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

Re: 64 small identical cubes are used to form a large cube [#permalink]

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Re: 64 small identical cubes are used to form a large cube [#permalink]

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15 May 2016, 01:35

Let the side of the cube is x. The area is X^3=64 X=4 , there are 4 cubes on each side To add one top layer of small cube all over the surface of the large cube. we have to add one cube at both ends of a side 1+4+1=6, the new cube will have =216 cubes.

The difference in the number of cubes we've added: 216−64=152

C

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Re: 64 small identical cubes are used to form a large cube
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15 May 2016, 01:35

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