1.
How many cubes have no face painted?
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?
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?
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?
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?
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?
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?
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?
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?
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?
Answer: Option 'A'
To find out total number of cubes we use this formula- (X)3
Implementation of formula: X = 4
(4)3 = 64