A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?

• Assuming the cube to be a solid one of 5cm side then its volume is 125 cu.cm
  
  When this cube is cut into small cubes of 1cm each then we will have 125 small cubes of side 1cm. If the outer surface of this cube is painted then we have 25*6 -> 150 faces of the small cubes painted.(Each surface would account to 25 small pieces)
  
  This cube is hollow with 1 cm side. The inner side of the hollow will have dimensions of 5 – 2 -> 3cm all around. The volume of this is 27 cu.cm and this many numbers of cubes are less in the total cubes if it were to be solid.
  
  Hence the actual number of 1cm cube now available is 125 – 27 = 98.
  
  Each of these cubes have 6 sides and hence the total number of sides for these 98 cubes is 98 * 6 = 588 faces. Of these we know 150 faces are painted. Hence, the number of faces not painted is 588 – 150 = 438 faces.
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• 36 cubes are unpainted.12 in 1 layer.so dere are 3 layers.
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• ans=9
  since it 5*5 cube with all sides colored there will be only 3*3 small cubes are left unpainted
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