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SSC CHSL Cube & Dice

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This page covers SSC CHSL Cube & Dice with complete concept notes, 20 graded practice MCQs, key points and exam-specific tips. Free to study.

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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

20graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

When a cube is unfolded, one face is marked as 'X'. If the unfolded net shows X on top, and adjacent faces are marked A, B, C, D (in clockwise order around X), which face is opposite to X?

Practice 2easy

A cube has six faces. Three faces meeting at a corner are colored Red, Blue, and Green. How many faces of the cube are NOT colored?

Practice 3easy

A cube has faces numbered 1 to 6. Face 1 is opposite to face 6, face 2 is opposite to face 5, and face 3 is opposite to face 4. If face 1 is on top and face 2 is facing you, which face is on the bottom?

Practice 4easy

A cube is unfolded into a net. The net shows six squares arranged in a cross pattern: one square in the center, one above it, one below it, one to the left, one to the right, and one more to the right of the right square. When this net is folded into a cube, which two faces will be opposite to each other?

Practice 5easy

A die is rolled and shows face value 5 on top. The face touching the ground shows 2. Which face is facing towards you?

Practice 6easy

A cube has faces numbered 1 to 6. When face 1 is on top and face 2 is facing you, face 3 is on your right. Which face is at the bottom?

Practice 7easy

A die shows 1, 2, and 3 on three faces meeting at one corner. What is the sum of the numbers on the three faces opposite to these?

Practice 8medium

A standard die shows opposite faces summing to 7. If a die is positioned with face 4 on top and face 1 facing north, which face is facing west?

Practice 9medium

A cube has six faces painted with colors: Red, Blue, Green, Yellow, Orange, and White. Red is opposite to Blue. Green is opposite to Yellow. If the cube is oriented with Red facing north and White on top, which color faces west?

Practice 10medium

A standard die shows opposite faces summing to 7. If a die is placed with 2 on top and 3 facing north, which number faces south?

Practice 11medium

A cube has faces numbered 1 to 6. When face 1 is on top and face 2 is facing you, face 3 is on your right. If the cube is now rotated such that face 3 is on top and face 1 is facing you, which face is on your right?

Practice 12medium

A dice is thrown and lands showing a certain face. The sum of the numbers on the top and bottom faces is 7. If the front face shows 2, and the left face shows 3, what is the sum of the numbers on the back and right faces?

Practice 13medium

Two dice are placed side by side. The left die shows 4 on top and 1 facing you. The right die shows 3 on top and 2 facing you. Both dice are standard (opposite faces sum to 7). What is the sum of the numbers on the right faces of both dice combined?

Practice 14hard

A cube has six faces. On one face is a single dot, on the opposite face are six dots. On another face are two dots, and on its opposite face are five dots. The remaining two opposite faces have three and four dots respectively. When the cube is rolled such that the face with one dot is on top and the face with two dots faces you, which face is on the bottom?

Practice 15hard

A standard die is placed on a table. You observe that faces showing 2, 3, and 5 are visible from your current angle. Based on standard die configuration (opposite faces sum to 7), which of the following statements is definitely true?

Practice 16hard

A cube is painted on all six faces with different colors. The cube is then cut into 27 smaller cubes of equal size (3×3×3 arrangement). How many of the smaller cubes have exactly two painted faces?

Practice 17hard

A cube has faces labeled 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. The cube is placed such that A faces north and C faces east. If the cube is then rotated 90° clockwise around the vertical axis (when viewed from above), which face now faces north?

Practice 18hard

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

Practice 19hard

An unfolded cube net shows faces labeled A, B, C, D, E, F arranged in a cross pattern: B-A-C in the middle row, with D above A, E below A, and F to the right of C. When folded, if face A is the bottom, which face is the top?

Practice 20hard

A cube has faces labeled 1 through 6. When face 1 is facing north and face 2 is facing up, face 3 faces east. If the cube is rotated 90° clockwise (when viewed from above), which face now faces north?

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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