Questions 21-25: A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size. 21. How many cubes are there which have no face painted ?

• Since all faces are painted, only small cubes which are in the middle of cube will have no color painted.
  Total smaller cubes=64
  Small cubes which are atleast 1 side is coloured
  = top(16 cubes)+ bottom(16 cubes)+ both sides(16 cubes)+ both sides adjacent to previous sides(8 cubes)=16+16+16+8=56
  so cubes with no paint=64-56=8
  answer is 8 cubes
  
• 9 years agoHelpfull: Yes(11) No(0)
• o Face Painted-------> (n-2)^3 * 1
  1 Face Painted-------> (n-2)^2 * 6
  2 Face Painted-------> (n-2)^1 * 12
  3 Face Painted-------> (n-2)^0 * 8 ALWAYS 8
• 9 years agoHelpfull: Yes(10) No(1)
• 3 colored faces-8 corners=8
  2 colored faces-2 per edge=2*12
  1 colored face-4 per face-4*6
  left-64-24-24-8=8 !
• 9 years agoHelpfull: Yes(3) No(1)
• use this formula , (x-2)^3 ,where x is the side of the bigger cube.
  i.e (4-2)^3 = 8
  Therefore, 8 cubes will not have no face painted.
• 9 years agoHelpfull: Yes(2) No(1)
• (n-2)^3
  here total number of small cube=64
  hence n=4
  then,(4-2)^3=8
  
• 9 years agoHelpfull: Yes(2) No(1)
• As given the large cube is cut 64 equal size cubes it means 64 is the net volume of the large cube hence.
  Let x is side of larger cube
  X(3)=64
  X=4
  Now side of cube with no painted surface
  4-2=2
  Now volume of this cube
  2(3)=8
  Hence this cube can be cut into 8 equal size cubes hence 8
  Ihope everyone understood
  
• 9 years agoHelpfull: Yes(2) No(0)
• (n-2)^3
  here total number of small cube=64
  hence n=4
  then,(4-2)^3=8
• 9 years agoHelpfull: Yes(1) No(0)
• sudhir sharma how did u get 4 in the formula?
• 9 years agoHelpfull: Yes(0) No(2)
• 10
  9*6= 54. total cubes having some color on them. So 64-54=10
  
• 9 years agoHelpfull: Yes(0) No(2)
• cut will be like 3*3*3. so in mid of the cube only 1 cube will be there whose no face painted .
• 9 years agoHelpfull: Yes(0) No(2)
• all the cubes are having atleast one face painted except the middle one.so the answer is 1
• 9 years agoHelpfull: Yes(0) No(3)
• use this formula , (x-2)^2 ,where x is the side of the bigger cube.
  i.e (4-2)^2 = 4
  Therefore, 4 cubes will not have no face painted.
• 9 years agoHelpfull: Yes(0) No(1)
• 27 cubes are there which have no face painted
  
• 9 years agoHelpfull: Yes(0) No(1)
• 16
  4*4*4=64
  if 6 faces are painted with 3 colors and when we cut the cube into 64 cubes then cubes which are inside are not get painted and the cout of those cubes will be 16
• 9 years agoHelpfull: Yes(0) No(1)