# CRE 3 - Coloring cube with single color | LR - Cubes

**Answer the next 4 questions based on the information given below.**

All the faces of a cube are painted with blue color. Then it is cut into 125 small equal cubes.

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having only one face colored?

- (a)
54

- (b)
8

- (c)
16

- (d)
24

Answer: Option A

**Explanation** :

Since a cube is cut into smaller cubes, the number of cuts hence pieces along each axis should be same.

If the number of pieces along each axis is p.

∴ p × p × p = 125

⇒ p = ∛125 = 5 pieces.

Below is the diagram representing these pieces.

When a bigger cube is cut into smaller cubes with n pieces along each axis.

⇒ Number of pieces with 1 side colored = 6(n – 2)^{2}.

⇒ Number of pieces with 2 sides colored = 12(n – 2).

⇒ Number of pieces with 3 sides colored = 8.

⇒ Number of pieces with 0 side colored = (n – 2)^{3}.

Here,

⇒ Number of pieces with exactly 1 side colored = 6(5 – 2)^{2} = 54.

⇒ Number of pieces with exactly 2 sides colored = 12(5 – 2) = 36.

⇒ Number of pieces with exactly 3 sides colored = 8.

⇒ Number of pieces with no side colored = (5 – 2)^{3} = 27.

Hence, option (a).

Workspace:

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having no face colored?

- (a)
27

- (b)
8

- (c)
36

- (d)
24

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

Hence, option (a).

Workspace:

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having exactly three faces colored?

- (a)
27

- (b)
8

- (c)
36

- (d)
24

Answer: Option B

**Explanation** :

Consider the solution to first question of this set.

Hence, option (b).

Workspace:

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having exactly two faces colored?

- (a)
27

- (b)
8

- (c)
36

- (d)
24

Answer: Option C

**Explanation** :

Consider the solution to first question of this set.

Hence, option (c).

Workspace:

**Answer the next 4 questions based on the information given below.**

All the faces of a cube are painted with blue color. Then it is cut into 343 small equal cubes.

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having only one face colored?

Answer: 150

**Explanation** :

Since a cube is cut into smaller cubes, the number of cuts hence pieces along each axis should be same.

If the number of pieces along each axis is p.

∴ p × p × p = 343

⇒ p = ∛343 = 7 pieces.

Below is the diagram representing these pieces.

When a bigger cube is cut into smaller cubes with n pieces along each axis.

⇒ Number of pieces with 1 side colored = 6(n – 2)^{2}.

⇒ Number of pieces with 2 sides colored = 12(n – 2).

⇒ Number of pieces with 3 sides colored = 8.

⇒ Number of pieces with 0 side colored = (n – 2)^{3}.

Here,

⇒ Number of pieces with exactly 1 side colored = 6(7 – 2)^{2} = 150.

⇒ Number of pieces with exactly 2 sides colored = 12(7 – 2) = 60.

⇒ Number of pieces with exactly 3 sides colored = 8.

⇒ Number of pieces with no side colored = (7 – 2)^{3} = 125.

Hence, 150.

Workspace:

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having no face colored?

Answer: 125

**Explanation** :

Consider the solution to first question of this set.

Hence, 125.

Workspace:

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having exactly three faces colored?

Answer: 8

**Explanation** :

Consider the solution to first question of this set.

Hence, 8.

Workspace:

**CRE 3 - Coloring cube with single color | LR - Cubes**

How many small cubes will be formed having exactly two faces colored?

Answer: 60

**Explanation** :

Consider the solution to first question of this set.

Hence, 60.

Workspace:

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