Member • Apr 22, 2012

Banashree PatraImagine a cubic array made up of an n*n*n arrangement of unit cubes: the cubic array is n cubes wide, n cubes high and n cubes deep. A special case is a 3*3*3 Rubik’s cube, which you may be familiar with. How many unit cubes are there on the surface of the n * n * n cubic array?
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Replies

Member • Apr 22, 2012
zeroAre you sure? This action cannot be undone. 
Member • Apr 23, 2012
please explain~on*kiyuzeroAre you sure? This action cannot be undone. 
Member • Apr 23, 2012
6*n^2  12*n + 8 for n > 1Banashree PatraImagine a cubic array made up of an n*n*n arrangement of unit cubes: the cubic array is n cubes wide, n cubes high and n cubes deep. A special case is a 3*3*3 Rubik’s cube, which you may be familiar with. How many unit cubes are there on the surface of the n * n * n cubic array?Are you sure? This action cannot be undone. 
Member • Apr 23, 2012
6n[sup]2[/sup]  12n + 8
I think it can also be expressed as, n[sup]3[/sup]  (n2)[sup]3[/sup]Are you sure? This action cannot be undone. 
Member • Apr 23, 2012
The second is more elegant. It represents the actual situation. What we are considering is the outer cube minus the (n2) cube within it. n^3 is the total number of unit cubes, (n2)^3 is the number of unit cubes in the contained cube. Aesthetically the second solution is more satisfying.silverscorpion6n[sup]2[/sup]  12n + 8
I think it can also be expressed as, n[sup]3[/sup]  (n2)[sup]3[/sup]Are you sure? This action cannot be undone.