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

• total no of smaller cubes= 25+25+15+15+9+9=98
  painted face of bigger cube=1=25 small faces
  total faces of smaller cube=98*6=588
  remaining unpainted faces=588-25=563
• 9 years agoHelpfull: Yes(6) No(0)
• vol of big cube= 5^3-3^3=98
  so no of small cube =98
  so no of faces in smallcube =98*6=588
  1 face of big cube is painted means 25 faces painted in small cube
  so unpainted face in small cube is =588-25= 563
• 9 years agoHelpfull: Yes(4) No(0)
• total no of smaller cubes= 25+25+15+15+9+9=98
  no. of phases of bigger cube painted=1 = 25 small cubes
  therefore total no of unpainted cubes=98-25=73
• 9 years agoHelpfull: Yes(1) No(0)
• Number of smaller cubes=25*2+15*2+9*2=98
  Number of faces of smaller cubes=98
  Number of faces of smaller cubes painted=25
  Number of unpainted faces=98-25=73
• 9 years agoHelpfull: Yes(0) No(0)
• volume of bigger cube 5*5*5= 125
  so there is 125 smaller cubes
  1 face is painted of bigger cube
  so unpainted smaller cubes 125-25=100
• 9 years agoHelpfull: Yes(0) No(0)
• how is it i mean 25 15 and 9???
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• one side of biger cubes has 25 faces of smaller cube
  bcoz 5*5
  and totle 588faces (98*6)
  (125-27=98)
  total no of sml cube is 98cm3/1cm3=98
  so 588-25=ans
• 9 years agoHelpfull: Yes(0) No(0)
• can anyone explain the answer a little more vividly! 25*2+15*2+9*2 ??
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• please explain this question............
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• 563 is the right answer.....
• 9 years agoHelpfull: Yes(0) No(0)
• 3*3*3-2*2*2=98
  98*6=588
  588-4*25=
  488
• 9 years agoHelpfull: Yes(0) No(0)
• Total no of cubes is 125 but this is hallow cube so total no of cube is 125-27=98 . 1 cube have 6 face . So total no of faces 98*6=588. Now 1 side is painted so 25 faces are already painted so total no unpainted faces are 588-25=563 is the ans.
• 9 years agoHelpfull: Yes(0) No(0)
• length of each side = 5cm + 2*1 cm=7cm
  to make each cube of length of 1 cm we have to cut that cube into 7 smaller cubes
  the unpainted smaller cubes= (7-2)^3 =125 [ .". (n-2)^3 ]
• 9 years agoHelpfull: Yes(0) No(0)
• 588-100=488
• 9 years agoHelpfull: Yes(0) No(1)
• corner cubes have 3 faces painted and 3 unpainted and 8 corners are there .so 8*3=24 faces
  12 edges are there on which each is having 3 cubes whose 2 faces are painted and 4 are unpainted=4*12*3=144.
  9 cubes are remaining on each face of big cube.so 1 painted and 5 unpainted in those faces=9*6*5=270
  so total no. of unpainted faces are= 24+270+144=438
• 9 years agoHelpfull: Yes(0) No(0)
• The Hallow cube volume = n3−(n−2)2, Here n is the number of small cubes lie on the big cube edge.
  Now n = 5 so Hallow cube volume = 53−(5−2)2=125−27=98
  So 98 small cubes required to make a hallow cube of size 5 cm. Now total surfaces = 6 x 98 = 588
  Now if the bigger cube is painted 1 side, total 1 x 25 small faces got paint. So remaining small faces which does not have paint after cutting is 588 - 25 = 563
• 9 years agoHelpfull: Yes(0) No(0)