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?
Show Hint
Mentally fold the net along the dashed lines, track which two shaded faces end up sharing an edge, and check whether their relative orientation matches cube (i) or cube (ii).
Only (i) can correspond to the unfolded cube in Panel I.
Only (ii) can correspond to the unfolded cube in Panel I.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
Show Solution
The Correct Option isA
Solution and Explanation
A cleaner way to check a net-versus-solid question like this is to work with adjacency and opposite-face relationships instead of corner rotations. When a net is folded into a cube, two squares joined directly by a fold line always become adjacent faces of the cube, sharing one edge, and squares that are two folds apart along the net can end up as opposite faces.
Map the net to face relationships: Trace the dashed fold lines in Panel I and note which shaded squares are directly joined. The square with the diamond shares a fold line with the square carrying a shaded triangle, so on the finished cube, the diamond face and this triangle face must sit right next to each other, meeting along one edge.
Test cube (i) for adjacency and orientation: In cube (i), the diamond face and the triangle face are indeed adjacent, sharing an edge, and the triangle's shaded corner touches the diamond's edge in the exact way the flat paper would produce once folded. This is consistent with the net.
Test cube (ii) for adjacency and orientation: In cube (ii), although the diamond and triangle faces are still adjacent, the shaded triangle occupies a different corner of its face than what folding the original net would give. Since flipping or spinning a rigid cube can never change which specific corners of two glued faces touch, this mismatch cannot be fixed by rotation, it is a genuine contradiction with the net.
Because cube (ii) shows an orientation that the paper folding cannot physically produce, it is eliminated, while cube (i) survives every check.
Let's summarize:
A fold line in the net always becomes a shared edge between two faces on the solid cube.
Rotating a finished cube never changes which corners of adjacent shaded shapes touch, so a wrong corner match in the picture cannot be explained away by rotation.
So only cube (i) is a valid fold of the net in Panel I, confirming option (A).
