Question

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?

• 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.

Hint:

Fold the net one face at a time, keeping track of which edges become shared with which faces, and check whether each candidate cube preserves that arrangement without any mirroring.

Answer 1

The Correct Option is B

Step 1: Identify all six faces of the net.
Panel I is a six-square net arranged as a central square with a square attached above it, a square attached below that, one more square attached below that one, and one square attached on each of its left and right sides. Taking the central square as the FRONT face, the square above it becomes the TOP face when folded up, the square below the front becomes the BOTTOM face, the square attached below that in turn becomes the BACK face (opposite the front), and the squares on the left and right become the LEFT and RIGHT faces respectively.

Step 2: Note each face's shading pattern before folding.
The FRONT face carries a thin stripe, the TOP face carries a triangular shaded corner, the BOTTOM face carries a thin stripe, the BACK face is split evenly into a shaded half and a plain half, the LEFT face is mostly shaded with a plain notch cut out of one corner, and the RIGHT face is mostly plain with a shaded block in one corner. Because LEFT and RIGHT sit as mirror-image arms on either side of the same FRONT face, their shaded regions must also come out as mirror images of each other once folded, never as identical copies.

Step 3: Fold mentally and track the shared edges.
When the net is folded into a cube, every crease becomes an edge shared by two faces, and the shaded pattern on each side of that crease must line up continuously across the edge, without flipping or mirroring, because a single sheet of paper cannot mirror itself while folding along a straight crease. This gives a reliable check: for any three mutually visible faces in an isometric drawing, the way their shaded regions meet at the shared corner must be traceable back to a single, non-mirrored crease-by-crease path through the original net.

Step 4: Apply the check to option (i).
In cube (i), the shaded corner on the visible left face and the shading carried onto the adjoining top and right faces do not continue into each other the way the net's creases require; reproducing them would call for one of the faces to be a mirrored version of its net pattern, which folding alone cannot produce. So cube (i) cannot be obtained from Panel I.

Step 5: Apply the check to option (ii).
In cube (ii), the three visible faces show shading that continues correctly across each shared edge exactly as dictated by the sequence of creases in Panel I, with no mirroring required anywhere. So cube (ii) is a valid folded form of the net.

Conclusion: Only cube (ii) can correspond to the unfolded net in Panel I, which is option 2.