we have two cubes which are joined to each other covering one face of each. and remaining faces oof both are colored with the different colors.
then the first cube is cut into 8 smaller cubes and another in 27 smaller cubes. what is the total number of faces having no color?

• ans : 145
  each cube having 6 faces
  for each cube 5 faces has color and one face for each has not
  1st cube divided into 8 smaller cubes so num of faces = 8*6 = 48
  in this 48 faces 5*4 = 20 faces having the color and 28 don't
  because if we divided a cube into 2^n smaller cubes (2^3 = 8) then each face of original cube is divided into 2^(n-1) smaller faces (2^2 = 4) [and inner faces also there]
  similarly 2nd cube divided into 27 smaller cubes so num of faces = 27*6 = 162
  in tiis 162 faces 5*9 = 45 faces having color and 117 don't
  total no of faces having no color = 28+117 = 145
• 10 years agoHelpfull: Yes(4) No(3)
• in 8 smaller cubes there are 4 cubes in all faces
  in 27 smaaler cubes there are 9 cubes in all faces
  therefore , totally 4+9 = 13 faces are not painted
• 10 years agoHelpfull: Yes(2) No(5)
• 4 faces having no colour,because 1 cube is of 3size and 1 is of 2size
• 10 years agoHelpfull: Yes(0) No(1)
• answer-13
  consider 1st cube -1)imagine we are looking cube from top , now we cut into 2 , now we have 2 parts,
  2)again cut into 2 parts , now we have 4 parts each ,)
  3)imagine we are looking from side , we again cut into 2 ,
  4)now we have total 8 cubs , which means we have properly cut one cube into 8 parts.
  so we have 4 pieces of cube which are blank..........(I)
  
  
  again same exercise for 2nd cube
  , 1)look from top , cut into 3 ,
  2)again cut into 3, now total we have 9 cubs, ok
  3)look from side again cut into 3 , now you will get 27 cube exactly , thats what we want.
  4)now we have total 9 cubs whose one side is blank ,
  now as you imagine you will get answer, i may do mistake , if i am wrong please tell me .
• 10 years agoHelpfull: Yes(0) No(0)
• ans:67
  for first 8 smaller cubes 14 faces and for next 27 cubes 53 faces having no color
• 10 years agoHelpfull: Yes(0) No(0)