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SSC CPO Cube & Dice

Study Material — 2 PYQs (2022–2022) · Concept Notes · Shortcuts

SSC CPO Cube & Dice is a frequently tested subtopic — 2 previous year questions from 2022–2022 papers are included below with concept notes, key rules and shortcut tricks.

2 PYQs
2022–2022
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8 Key Points
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Previous Year Questions

SSC CPO Cube & Dice — Past Exam Questions

2 questions from actual SSC CPO papers · all shown free · click option to reveal solution

Exam Q 12022Previous Year Pattern

A cube has faces numbered 1 to 6. Face 1 is opposite to face 6, and face 2 is opposite to face 5. When face 3 is on top, which face is at the bottom?

Exam Q 22022Previous Year Pattern

A standard die shows opposite faces summing to 7. If face showing 2 is facing you, and face showing 3 is on top, which face is facing away from you?

Concept Notes

Cube & Dice— Rules & Concept

Core ConceptRead 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.

Worked ExampleSolve 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).

4
Step 4

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

5
Step 5

Face B is opposite to face D.

6
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.

Exam TrapsCommon mistakes students make — avoid these

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 to Remember

  • 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-Specific Tips

  • 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
Practice MCQs

Cube & Dice — Practice Questions

7graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

Two dice are placed such that face A of the first die is adjacent to face B of the second die. If face A shows 3 and face B shows 5, and both dice follow the standard rule (opposite faces sum to 7), which of the following is definitely true?

Practice 2easy

A cube has six faces labeled with letters: A, B, C, D, E, and F. It is known that A is opposite to B, C is opposite to D, and E is opposite to F. When face A is facing north and face C is facing east, which face is facing down?

Practice 3easy

A standard die is placed on a table. The face showing 1 is on top. The face showing 2 is facing you. Which number is on the bottom face of the die?

Practice 4easy

A cube is painted on all six faces with different colors. The cube is then cut into 8 smaller cubes of equal size. How many of the smaller cubes will have exactly 3 painted faces?

Practice 5medium

A cube has six faces. On one face, the number 1 is written; on the opposite face, the number 6 is written. On another face, the number 2 is written; on its opposite face, the number 5 is written. The remaining two opposite faces have 3 and 4 written on them respectively. When the cube is placed such that face 1 is on top and face 2 is facing you, which number is on the bottom face?

Practice 6medium

A cube has six faces labeled with numbers 1 through 6. It is known that: (i) 1 and 6 are on opposite faces, (ii) 2 and 5 are on opposite faces, (iii) When 1 is on top and 2 is facing you, 3 is on your right. The cube is now placed with 4 on top. Which number is facing you?

Practice 7medium

A standard die has opposite faces summing to 7. A die is placed on a table with face showing '2' on top. The die is rolled forward (away from you) once, then rolled to the right once. After these two rolls, which number is now on top?

60-Second Revision — Cube & Dice

  • 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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