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A cube of side 5 cm is painted on all its sides . If it is s

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A cube of side 5 cm is painted on all its sides . If it is s [#permalink] New post 31 Jan 2012, 17:03
A cube of side 5 cm is painted on all its sides . If it is sliced into 1 cubic centimeter cube how many 1 cubic centimeter cubes will have exactly one of their sides painted ?

Could someone please explain the logic behind this problem ?
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Re: A cube of side 5 cm is painted on all its sides . If it is s [#permalink] New post 31 Jan 2012, 18:17
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This is definitely one of those tricky visualization problems :)

Imagine just one face of the 5x5 cube. (I'm imagining this massive Rubik's cube :-D )

Which of the 1x1 cubes will have paint on only one face? Only those which are not on the
edges - these will share a painted face with another side. The cubes that are not part of the
edge form a 3x3 grouping of 1cm cubes.

Therefore each face has 9 cubes that are painted one color.

Since there are 6 faces we get 6x9 = 54.

Hope that helps!
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Re: A cube of side 5 cm is painted on all its sides . If it is s [#permalink] New post 01 Feb 2012, 00:09
Thanks a lot chris for the solution.
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Re: A cube of side 5 cm is painted on all its sides . If it is s [#permalink] New post 01 Feb 2012, 04:09
Why are we assuming that the cude is of 1 X 1 CM only? It is not mentioned in the question stem & we could have a cube of the same volume using various dimensions such as 0.1 x 2 x 5 thus changing our calculation completely
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Re: A cube of side 5 cm is painted on all its sides . If it is s [#permalink] New post 01 Feb 2012, 22:25
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boomtangboy wrote:
Why are we assuming that the cude is of 1 X 1 CM only? It is not mentioned in the question stem & we could have a cube of the same volume using various dimensions such as 0.1 x 2 x 5 thus changing our calculation completely


'Cube' implies that every edge has the same length. So, length = breadth = height = 1

You are thinking 'cuboid' - a rectangular parallelepiped
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Re: A cube of side 5 cm is painted on all its sides . If it is s   [#permalink] 01 Feb 2012, 22:25
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