A paper shown in Panel I is folded along the dashed lines (- - -) to construct a
cube. The shaded regions shown in Panel I appear on the outer surface of the cube.
Referring to cubes shown in Panel II, which one of the options is correct?
Options:
(A) Only (i) can correspond to the unfolded cube in Panel I.
(B) Only (ii) can correspond to the unfolded cube in Panel I.
(C) Both (i) and (ii) can correspond to the unfolded cube in Panel I.
(D) Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2026 Q.7)**
**1. Intuitive Physical Setup & Given Parameters**:
A flat 2D net of a cube shown in Panel I is folded along dashed lines to construct a 3D cube. Shaded patterns appear on specific faces. We must determine which of the perspective views in Panel II (i or ii) can be formed.
**2. Step-by-Step Spatial Deduction**:
1. **Opposite vs Adjacent Faces in Cube Net**:
- In a standard cube net, faces separated by one intervening square become opposite faces on the folded cube, and opposite faces can never share an edge or be visible simultaneously in a standard 3-face perspective view.
2. **Verifying Edge Adjacencies**:
- Tracing the folding of Panel I:
- When the shaded regions fold around the vertex shared by the three visible faces in cube (i), their relative orientations and meeting edges match the net precisely.
- In cube (ii), one of the shaded patterns has an inverted orientation relative to the adjacent edge, creating a chirality/handedness violation that cannot be formed by rigid folding without turning the paper inside-out.
3. Therefore, only configuration **(i)** correctly represents the folded cube.
**3. Comprehensive Options & Distractor Analysis**:
- **(A) Only (i) can correspond to the unfolded cube in Panel I**: ✅ **CORRECT**. Edge meeting rules and surface orientation match only (i).
- **(B) Only (ii) can correspond to the unfolded cube in Panel I**: ❌ **INCORRECT**. (ii) violates edge alignment of the shaded facets.
- **(C) Both (i) and (ii) can correspond to the unfolded cube in Panel I**: ❌ **INCORRECT**. (ii) is chiral/inconsistent.
- **(D) Neither (i) nor (ii) can correspond to the unfolded cube in Panel I**: ❌ **INCORRECT**. (i) is fully valid.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A**
- **Exam Takeaway**: When folding paper cubes, test the cyclic order (clockwise vs counter-clockwise) of features around the corner where 3 faces meet to detect chirality mismatches instantly.
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