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

Answer: Option A

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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.

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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).

Answer: Option A

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Explanation :

Consider the solution to first question of this set.

Hence, option (a).

Answer: Option B

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Explanation :

Consider the solution to first question of this set.

Hence, option (b).

Answer: Option C

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Explanation :

Consider the solution to first question of this set.

Hence, option (c).

Answer: 150

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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.

Answer: 125

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Explanation :

Consider the solution to first question of this set.

Hence, 125.

Answer: 8

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Explanation :

Consider the solution to first question of this set.

Hence, 8.

Answer: 60

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Explanation :

Consider the solution to first question of this set.

Hence, 60.