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guerrero25
Joined: 10 Apr 2012
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Posts: 244
Updated on: 16 Apr 2013, 23:28
Originally posted by guerrero25 on 16 Apr 2013, 13:51.
Last edited by Bunuel on 16 Apr 2013, 23:28, edited 1 time in total.
Last edited by Bunuel on 16 Apr 2013, 23:28, edited 1 time in total.
Edited the question.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (01:52) correct
46%
(02:08)
wrong
based on 662
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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
A. 64
B. 128
C. 152
D. 216
E. 256
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: \(216-64=152\)
C
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: \(216-64=152\)
C
aceacharya
Joined: 04 Mar 2013
Last visit: 10 Feb 2016
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Location: India
Concentration: Strategy, Operations
Schools: Booth '17 (M)
GMAT 1: 770 Q50 V44
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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
All add up to 96+48+8=152
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
General Discussion
guerrero25
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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aceacharya
Hi! I did not understand why you did 4^2, and why 8 more cubes are required at the corners.
vjns
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
Posts: 35
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.
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.
PareshGmat
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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
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
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
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
Posts: 48
Zarrolou
Why you have mentioned 'area' where as you have calculated 'volume'?
guerrero25
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
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 : 216-64 =152.... Ans C
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 : 216-64 =152.... Ans C
guerrero25
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.
PreiteeRanjan
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guerrero25
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.
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