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:

Use the shaded diamond face as a fixed reference point, then check whether the neighboring faces' shading lands in the same rotational position (never mirrored) as a genuine fold of the net would produce.

Answer 1

The Correct Option is A

Step 1: Label every face of the net in Panel I.
The net is a chain of six squares joined edge to edge along the marked dashed fold lines, one flap attached near the top of the chain and one flap attached near the bottom, with four squares forming the main column in between. Each square carries its own shaded mark: a diagonal triangle, a solid small square, a rotated shaded diamond, and further diagonal triangles on the two end flaps. The clearest, most identifiable face is the one carrying the shaded diamond in the middle of the strip, since a diamond (a square rotated 45 degrees) cannot be confused with any triangular mark, and this same diamond appears on the front face of both candidate cubes (i) and (ii) in Panel II.

Step 2: Use the diamond face as a fixed reference.
Since both cube (i) and cube (ii) place the diamond on the same visible (front) face, the diamond face alone cannot distinguish between them. The two candidate cubes must instead be told apart by the faces adjacent to the diamond, that is, the top face and the right side face visible in the drawing, and by how each neighboring face's own diagonal shading is oriented once the net is actually folded.

Step 3: Track which net-faces fold up against the diamond face, and in what orientation.
Folding a strip of squares along their shared edges only ever rotates a face about that shared hinge, it never mirrors or flips the pattern printed on the paper. So each neighboring face keeps a fixed, predictable orientation relative to the diamond face once folded, determined entirely by which edge of the net it was hinged from. Walking through the net from the diamond square outward to its immediate neighbors on the strip shows that the adjacent triangular shading lands in the upper-right area of the top face and the lower portion of the right face, exactly the placement drawn in cube (i).

Step 4: Check cube (ii) against the same folding.
Cube (ii) shows the same diamond front face, but its neighboring triangular shading sits in the mirror-image position compared to what the physical fold produces, the kind of left-right reversal that would only occur if the paper's shaded side were flipped over before folding. Since the problem states the shaded regions must appear on the outer surface after folding this specific net (not a mirrored version of it), cube (ii) cannot be produced.

Final Answer:
Only cube (i) is consistent with folding the given net, so option (A) is correct. \[ \boxed{\text{Option (A)}} \]