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Cube & Dice

AFCAT · Logical Reasoning

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Core Concept

Read this first — the foundation of the topic

A cube is a three-dimensional object with 6 faces, 12 edges, and 8 vertices. Each face is a square. In SSC CGL exams, cube and dice questions test your ability to visualize how a flat pattern folds into a 3D shape or how a cube looks when rotated. Key Rules for Cubes: 1.

Opposite faces never touch each other when the cube is folded 2. Adjacent faces share a common edge 3. When a cube is cut, count the pieces formed 4.

In dice problems, opposite faces always add up to 7 (1-6, 2-5, 3-4) Main Question Types: - Net to Cube: Given a flat pattern, identify which cube it forms - Cube Views: Different views of the same cube from various angles - Dice Problems: Find opposite faces or adjacent faces - Cube Cutting: Calculate pieces when cube is cut by planes Shortcut for Net Problems: Use the 'Corner Method' - pick any corner in the net and trace which three faces meet at that corner. In the answer choices, the same three faces must meet at one corner. This eliminates wrong options quickly.

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Worked Example

Solve this step-by-step before moving on

1

Step 1

Identify which faces are opposite to each other in the net.

2

Step 2

Faces that are separated by exactly one face in between are opposite.

3

Step 3

In the net A-B-C-D, face A is opposite to face C (one face B in between).

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Step 4

Face E is above B, so E is opposite to F (which is below C).

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Step 5

Face B is opposite to face D.

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Step 6

Since A is at bottom, its opposite face C will be at top. Answer: Face C For Dice Problems: Remember the standard dice pattern: 1 opposite 6, 2 opposite 5, 3 opposite 4. If you see faces 1, 2, 3 meeting at a corner, you know 6, 5, 4 meet at the opposite corner. Cube Cutting Formula: If a cube is cut by n planes parallel to faces: Total pieces = (n₁ + 1) × (n₂ + 1) × (n₃ + 1), where n₁, n₂, n₃ are cuts along length, breadth, and height. Common Mistake: Students often confuse adjacent faces with opposite faces. Remember - opposite faces never appear together in any single view of a cube. If two faces are visible together in a view, they cannot be opposite faces.

🔑 Key Points

A cube has 6 faces, 12 edges, and 8 vertices with each face being a perfect square
Opposite faces in a cube never share an edge or vertex with each other
In standard dice, opposite faces always sum to 7: (1,6), (2,5), (3,4)
Net to cube problems: faces separated by one face in between are opposite
Corner method: three faces meeting at any corner must be consistent in all views
Cube cutting formula: pieces = (cuts+1) along each dimension multiplied together
Adjacent faces share a common edge and can be seen together in cube views
If two faces appear together in any view, they cannot be opposite faces

📌 Exam Facts

Standard dice opposite pairs sum to 7: 1-6, 2-5, 3-4
A cube has exactly 6 faces, 12 edges, and 8 vertices
Each vertex of a cube is formed by exactly 3 faces meeting together
Maximum 3 faces of a cube can be visible from any single viewpoint
In net problems, faces separated by exactly one face are opposite
Cube cutting by n parallel planes creates (n+1) pieces in that direction
Each face of a cube is adjacent to exactly 4 other faces
Each edge of a cube is shared by exactly 2 faces

🚀 60-Second Revision

Remember: Opposite faces never appear together in any cube view
Formula: Dice opposite pairs always sum to 7 (1-6, 2-5, 3-4)
Trick: Use corner method - trace three faces meeting at any corner
Pattern: In nets, faces with one face gap between them are opposite
Cutting: Total pieces = (cuts+1) multiplied for each dimension
Trap: Don't confuse adjacent faces with opposite faces
Quick check: Maximum 3 faces visible from any single angle

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