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 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

900

500

488

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
• 13 years agoHelpfull: Yes(44) No(1)
• Size of big cube = 5cm
  Total volume of the big cube = 5*5*5 = 125cm^3
  
  Size of the hollow cube = 3cm
  Volume of the hollow space = 3*3*3 = 27cm^3
  
  so, 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 = 98 / 1 = 98
  
  Each cube has 6 faces, so 98 cubes have = 98*6 faces = 588
  
  each big side has 25 faces of the small cubes.So,
  The four sides of the big cube have 100 painted faces.
  
  So, total unpainted faces = 588 - 100 = 488
• 13 years agoHelpfull: Yes(4) No(0)
• How are you calculating size of hollow cube inside the big cube =3 cm, please elaborate
  
• 9 years agoHelpfull: Yes(2) No(0)
• small cubes in one side=5*5=25
  Total small cubes=25*6=150
  
  Two surface not painted so all faces
  of small cubes=25*2*6=300
  
  4 faces painted only one side=25*4*5=500
  
  Total unpainted surface=500+300=800
• 13 years agoHelpfull: Yes(0) No(20)
• how did u get each big side has 25 faces of the small cubes???
  
• 9 years agoHelpfull: Yes(0) No(0)
• Reena each face of a cube is equivalent to a square. now the area of a square is square(side). thus we consider 4 such squares each with area 5*5=25.
• 9 years agoHelpfull: Yes(0) No(0)