**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?

**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**

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