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?
Figure Q.7 — Panel I (net) and Panel II (cubes) — approximate reconstruction
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:
B
Step-by-Step Solution & Explanation
Folding the cross-shaped net brings the arm faces up around the central face; three faces then meet at each vertex, and their shading pattern and handedness become fixed.
Cube (ii) shows the diagonally-split (triangular) shaded face adjacent to a plain face in exactly the orientation the net produces — it is realisable.
Cube (i) requires the two block-shaded faces to meet at a vertex with the shaded corners pointing in a combination that is the mirror image of what the net generates. A mirror image cannot be obtained by folding alone (folding preserves chirality), so (i) is impossible.
Hence only (ii) is possible → (B).
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