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64 small identical cubes are used to form a large cube
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Updated on: 17 Apr 2013, 00:28
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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
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Originally posted by guerrero25 on 16 Apr 2013, 14:51.
Last edited by Bunuel on 17 Apr 2013, 00:28, edited 1 time in total.
Edited the question.




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Re: 64 small identical cubes are used to form a large cube
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16 Apr 2013, 14:58
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: \(21664=152\) C
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Re: 64 small identical cubes are used to form a large cube
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17 Apr 2013, 00:32
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: abigcubeisformedbyrearrangingthe160colouredand99424.htmlalargecubeconsistsof125identicalsmallcubeshow110256.htmlHope it helps.
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Re: 64 small identical cubes are used to form a large cube
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17 Apr 2013, 05:43
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
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Re: 64 small identical cubes are used to form a large cube
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21 Sep 2013, 05:08
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
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.



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Re: 64 small identical cubes are used to form a large cube
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21 Sep 2013, 06:20
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
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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 Extra cube required = 216  64 = 152 Hence, C is the answer.
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Re: 64 small identical cubes are used to form a large cube
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23 May 2014, 03:07
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
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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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28 Jun 2017, 11:13
Zarrolou wrote: 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: \(21664=152\)
C Why you have mentioned 'area' where as you have calculated 'volume'?



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Re: 64 small identical cubes are used to form a large cube
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06 Jul 2018, 01:19
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 Given 64 small cubes are used to form a large cube. Consider the smaller cube with dimensions of 1 unit each. We get volume of each smaller cube = 1 cubic unit The larger cube will have a volume = 64 cubic units = 4^3 cubic units. Hence the larger cube has dimensions as 4 units & is made of 64 cubes. Now if we want to add a top layer of cubes on each surface, hence we are increasing the dimensions of the larger cube by 1 unit in all directions. Hence the height of the cube will be increased by 1 unit on the top & by 1 unit on the bottom. Similarly for length & width. We get a new larger cube of dimensions 6 units. Its volume = 6^3 = 216 cubic units & is made of 216 cubes. Therefore the no. of additional cubes required = 216  64 = 152 cubes Answer C. Thanks, GyM
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Re: 64 small identical cubes are used to form a large cube
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10 Nov 2018, 17:59
According to the Q, we have a cube stack of 4 at every axis of a 3d plane : 4^3=64 As we need to add 1 layer at each side we need a total stack of (1+4+1)^3 = 216 cubes Thus , small cubes required to meet the cond : 21664 =152.... Ans C
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Re: 64 small identical cubes are used to form a large cube
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22 Nov 2018, 15:13
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 It's a 4 x 4 x 4 cube. An extra layer will make it 6 x 6 x 6 cube (a cube on each side will increase each edge by 2 cubes) Difference = 6^3  4^3 = 216  64 = 152 C is my answer.



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Re: 64 small identical cubes are used to form a large cube
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05 Jun 2019, 01:20
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 simple math: small cube+64 should be equals to larger cube , a number of cubic form. so starting from option A 64*64 is not a cube number proceeding direct to answer option,as i already sovled, 152+64=216=6^3,so solved. ONE KUDO IF YOU LIKE THE METHOD.




Re: 64 small identical cubes are used to form a large cube
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