A block of wood in the form of cuboid of dimensions 6*7*14* has all its six faces painted pink if the wooden is cut into 504 cubes of dimension 1*1*1 how many of these would have pink paint on minimum one side of them

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if you have got 504 small cubes then the Cuboid has size 6 * 6 * 14 not 6 * 7 * 14. What is correct? If cuboid is 6 * 6 * 14 then the ANSWER is : 504 - (6-2)*(6-2)*(14-2) = 504 - 192 = 312. If cuboid is 6*7*14 then answer is 348
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See diagram enclosed to understand

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2014-07-29T23:37:07+05:30

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SEE Figure enclosed/attached diagram. to understand.
a = 6        b = 7      c = 14                              ( check if  b = 6 or 7)
Volume of big cuboid = 6 * 7 * 14 =  588 units
Volume of small cuboid  =  1 * 1 * 1 = 1 unit
So we get  Cuboid volume / small cube volume  =  588 number of small cubes when we cut the big one.
The cuboids whose surface is not exposed to the paint or whose surface we donot see from outside will be calculated as follows.    We imagine small cubes 1 by 1 by 1 are arranged to form the big cuboid of  a * b * c .  Layer of One cube on each surface is exposed to paint.  There are two equal surfaces on oppposite sides of cuboid. Each side length or breadth or height, you have 2 cubes seen from two opposite faces of cuboid.

 The cubes hidden inside and not seen at all are
             (a - 2 )  * (b -2 )  * (c -2 )   = 4 * 5 * 12    = 240  cubes
 small Cubes which are seen on the surfaces of big cuboid = 588 - 240  = 348
THese many cubes have pink on at least one side.

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