Problems based on Cubes and Dice Question Figures and answers : Non Verbal

  • Directions: (Questions 1 to 10) A solid cube of each side 8 cm, has been painted red, blue and black on pairs of opposite faces.
    It is then cut into cubical blocks of each side 2 cm.

     
  • 1. How many cubes have no face painted? 
   A.) 0
   B.) 4
   C.) 8
   D.) 12

Answer: Option 'C'

Cubes have only one face painted = Central cubes : In middle of faces & has only one coloured side.
We can find out the total number of cubes with singe color on any side with this formula: 6(X-2)2
Implementation of formula: X = 4
6(4-2)2 = 6(2)2 = 24

  • 2. How many cubes have only one face painted?
   A.) 8
   B.) 16
   C.) 24
   D.) 28

Answer: Option 'C'

Cubes have only one face painted = Central cubes : In middle of faces & has only one coloured side.
We can find out the total number of cubes with singe colour on any side with this formula: 6(X-2)2
Implementation of formula: X = 4
6(4-2)2 = 6(2)2 = 24

  • 3. How many cubes have only two faces painted? 
   A.) 8
   B.) 16
   C.) 24
   D.) 20

Answer: Option 'C'

Cubes have only two faces painted = Middle Cubes: In middle of edges and have two coloured sides.
We can find out the total number of cubes with singe colour on any side with this formula: 12(X-2)
Implementation of formula: X = 4
12(4-2) = 12(2) = 24

  • 4. How many cubes have only three faces painted? 
   A.) 0
   B.) 4
   C.) 6
   D.) 8

Answer: Option 'D'

Cubes have only three faces painted = Corner cubes : Cubes on corners and have three coloured sides.
A cube can have only 8 cut-corner cubes with colours on three sides. Hence answer will be always the same = 8
12(4-2) = 12(2) = 24

  • 5. How many cubes have three faces painted with different colours? 
   A.) 0
   B.) 4
   C.) 12
   D.) 8

Answer: Option 'D'

Cubes have three faces painted = Corner cubes : Cubes on corners and have three coloured sides.
A cube can have only 8 cut-corner cubes with colours on three sides. Hence answer will be always the same = 8.

  • 6. How many cubes have two faces painted red and black and all other faces unpainted?
   A.) 0
   B.) 8
   C.) 12
   D.) 14

Answer: Option 'B'

Cubes have two faces painted red and black and all other faces unpainted = 4+4 = 8

  • 7. How many cubes have only one face painted red and all other faces unpainted?
   A.) 0
   B.) 14
   C.) 12
   D.) 8

Answer: Option 'D'

Cubes have only one face painted red and all other faces unpainted = Central Cubes of Red Face = 4+4 = 8

  • 8. How many cubes have two faces painted black? 
   A.) 2
   B.) 4
   C.) 8
   D.) None

Answer: Option 'D'

None

  • 9. How many cubes have one face painted blue and one face painted red? (the other faces may be painted or unpainted? 
   A.) 16
   B.) 14
   C.) 8
   D.) 0

Answer: Option 'C'

Cubes have one face painted blue and one face painted red? (the other faces may be painted or unpainted = 4+4 = 8

  • 10. How many cubes are there in all? 
   A.) 64
   B.) 56
   C.) 40
   D.) 32

Answer: Option 'A'

To find out total number of cubes we use this formula- (X)3
Implementation of formula: X = 4
(4)3 = 64