A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 1 face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a) 900 b) 488 c) 563 d) 800

• The big cube is completely hollow.. But, the thickness of
  its side is 1cm & this is made up of smaller cubes.
  
  Just like the walls of a room. The room is hollow, but, its
  thickness is due to smaller bricks. The 4 walls of this room
  is painted from the outside. And, you are asked totally how
  many sides of all the bricks are now unpainted.
  
  First, you need to know how many bricks (small cubes) are there.
  
  Size of big cube = 5cm
  Total volume of the big cube = 5*5*5 = 125cm^3
  
  Size of the hollow cube inside the big cube = 3cm
  Volume of the hollow space inside the big cube = 3*3*3 = 27cm^3
  
  Therefore, volume occupied by small cubes (or volume of
  thickness) = 125 - 27 = 98cm^3
  
  Size of each small cube = 1cm
  Volume of each small cube = 1*1*1 = 1cm^3
  Total number of small cubes in wall = 98 / 1 = 98
  
  In short, 98 small cubes make up the wall of the big cube.
  Each cube has 6 faces, so 98 cubes have = 98*6 faces = 588
  
  The four sides of the big cube have 100 painted faces.
  Because each big side has 25 faces of the small cubes.
  
  Therefore, total unpainted faces = 588 - 100 = 488
• 12 years agoHelpfull: Yes(114) No(16)
• 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 (c)
• 14 years agoHelpfull: Yes(89) No(61)
• total no of cubes in solid cube =5^3
  total no of cubes in given hollow cube = 5^3-3^3=98
  total no of faces =98*6=588
  total faces painted = 25*4=100
  therefore faces unpainted =588-100=488
• 14 years agoHelpfull: Yes(47) No(36)
• answer is 563
  no of cubes of 1cm size is
  5^3-3^3=98
  no of faces 98*6=588
  if one side is painted then 5*5=25 surfaces is paintedremaining are unpainted..
  so 588-25=563
• 14 years agoHelpfull: Yes(14) No(15)
• total no of cubes in solid cube =5^3
  total no of cubes in given hollow cube = 5^3-3^3=98
  total no of faces =98*6=588
  since one face of big cube painted total faces painted = 25
  therefore faces unpainted =588-25=563
• 14 years agoHelpfull: Yes(12) No(13)
• hello mahadev,
  can u explain why you have 5^3-3^3.
  the 3^3 how comes? please explain briefly
• 12 years agoHelpfull: Yes(2) No(1)
• 488
  for detailed solution see previous pages
• 14 years agoHelpfull: Yes(1) No(19)
• plzz explain rishi
• 11 years agoHelpfull: Yes(1) No(0)
• the formula is {(n^3-(n-2)^3)*6}-(no of faces painted * n^2) here n=5 and no of faces painted =1 so putting the value the ans is =563
• 10 years agoHelpfull: Yes(1) No(1)
• answer is 563
  588-25=563
• 10 years agoHelpfull: Yes(1) No(1)
• total no of cubes in solid cube =5^3
  total no of cubes in given hollow cube = 5^3-3^3=98
  total no of faces =98*6=588
  since one face of big cube painted total faces painted = 25
  therefore faces unpainted =588-25=563
• 10 years agoHelpfull: Yes(0) No(2)
• 488
  x=5;
  t=1,s=1
• 5 years agoHelpfull: Yes(0) No(0)
• Hollow cube 5 * 5 * 5
  
  Assuming thickness internal
  
  thickness = 1cm would be each side
  
  5 - 1 - 1 = 3
  
  so available size = 3 * 3 * 3
  
  Total 1 * 1 * 1 size 27 cubes will be there
  
  A cube has 6 faces
  
  so total faces of 1 * 1 * 1 size cubes = 27 * 6 = 162
  
  Faces on outer side of Large cubes = 9 * 6 = 54
  
  faces of the smaller cubes remain unpainted = 162 - 54
  
  = 108
• 5 Months agoHelpfull: Yes(0) No(0)