a hollow cube of size 5 cm is taken of thickness 1 cm. it is made of smaller cubes of 1 cm. if 1 face of outer surface of the cube are painted. find how many total faces of the smaller cube remain unpainted

• Total number of small cubes=98
  Total number of faces 98*6=588
  
  Now one face of outer cube is painted hence 25 faces got painted
  => total faces of small cube remain unpainted=588-25=563
  
  Hence answer is 563
  
  Correct me if I am wrong
• 10 years agoHelpfull: Yes(10) No(3)
• hollow cube volume=n^3 - (n-2)^2
  n > no of small cubes
  n=5 > 5^3-(5-2)^2=98
  i.e. 98 small cubes
  total surfaces = 6*98=588
  if bigger cube is painted 4 sides i.e. 4*25=100 small faces got paint
  face does not paint=588-100=488
• 10 years agoHelpfull: Yes(6) No(3)
• Volume of Big Cube considering it is not hollow = L^3 = 5*5*5 = 125 cm^3
  Size of hollow cube (considering 1 cm thickness on two faces of large cube = 5-2 = 3cm
  Volume of hollow cube = 3*3*3 = 27 cm^3
  
  So Total Volume filled up by smaller cubes = Volume of Larger Cube - Volume of hollow cube = 125 - 27 = 98 cm^3
  Volume of 1 small cube = 1*1*1 = 1 cm^3
  Total number of small cubes in the larger cube = 98/1 = 98
  and Number of faces of 98 small cubes (6 faces each cube has) = 98*6 = 588 faces
  
  Total Surface area of 6 faces of larger cube painted = 6*L^2 = 6*5*5 = 150cm^2
  Surface area of one face of small cube = 1*1 = 1cm^2
  Number of faces of small cube painted = 150/1 = 150 faces
  
  => Hence number of faces of the smaller cubes remain unpainted = 588-150 = 438
• 10 years agoHelpfull: Yes(6) No(0)
• total small cubes required is 5^3-3^3=588
  1face of outer surface of cube is painted=so small 25 are required for that
  unpainted small cubes is 588-25=563
• 10 years agoHelpfull: Yes(5) No(2)
• ans : 488
• 10 years agoHelpfull: Yes(1) No(2)
• 475 faces of smaller cubes remain unpainted.
• 10 years agoHelpfull: Yes(0) No(1)
• total small cubes required is 5^3-3^3=588
  1face of outer surface of cube is painted=so small (25-9) are required for that
  unpainted small cubes is 588-16=572
• 10 years agoHelpfull: Yes(0) No(0)
• total number of blocks=(5*5*5)-(3*3*3)=98
  so total no of faces of smaller cubes=98*6=588
  and among all these faces one face of bigger cube is painted so totally 25 faces of small cubes r painted
  it means total unpainted faces=588-25=563
• 10 years agoHelpfull: Yes(0) No(0)