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Question

Hi everyone, i need help with the qns below.

A cube of sides x cm is painted blue on all six faces. If the cube is divided into x^3 smaller 1 cm cubes, find in terms of x, the number of cubes that have exactly
(a) 3 blue faces,
(b) 2 blue faces,
(c) 1 blue face and
(d) no blue faces.

 

Thanks in advance!

Answer

Hope it is clear enough

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Nice representation.. But the two surface, green color , should be 12 edges.

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So it should be 12 edges instead?

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I counted 12 edges with 2 color surfaces,

2 color edge

 

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okay thanks!

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The answers for (b) and (d) are 12(x – 2) and (x – 2)(x – 2)(x – 2) respectively.

http://nrich.maths.org/2322&part=solution

 

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