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:

Find two faces that share an edge in the net (the diamond face and the shaded-triangle face) and check that the shading crosses their shared edge in the same direction after folding, without flipping the paper over.

Answer 1

The Correct Option is A

Step 1: Understand the setup.
Panel I shows a flat net of six squares joined edge to edge, with dashed fold lines. When folded along these lines, the net closes up into a cube, and every shaded mark on the net becomes a mark on one face of that cube. Panel II shows two finished cubes, (i) and (ii), and we must decide which of them, if either, could really be the result of folding the exact net in Panel I.

Step 2: Pick two faces that share an edge in the net.
The square carrying the gray diamond and the square carrying the diagonally shaded triangle sit right next to each other in the net, joined along one common edge before folding. Because they already share an edge on the flat net, they must still share an edge once the cube is formed, and the marks on them must sit at a fixed angle to each other, since folding a single sheet of paper cannot flip one face over relative to its neighbor.

Step 3: Track the orientation across the fold.
Trace the shared edge between the diamond square and the triangle square, and note which corner of the triangle touches that shared edge, and which side of the diamond faces it. When the net is folded so the diamond ends up on the top face of the cube, the triangle square swings down to become an adjacent side face, carrying its shading with the same handedness it had on the flat sheet, since a simple fold never mirrors the paper.

Step 4: Compare with cube (i).
In cube (i), the diamond sits on the top face and the shaded triangle sits on the adjacent visible side face, with the triangle's shaded corner touching the shared edge in the same sense that was traced from the net in Step 3. This matches exactly what folding Panel I produces.

Step 5: Compare with cube (ii).
In cube (ii), the same two faces (diamond on top, triangle on the side) appear, but the triangle's shaded half is mirrored compared to what Step 3 predicts. Getting this mirrored version would need the paper to be flipped over before folding, which is not a valid paper fold. So cube (ii) cannot come from the net in Panel I.

Final Answer:
Only cube (i) is a valid fold of the net shown in Panel I. \[ \boxed{\text{Option (A): Only (i) can correspond to the unfolded cube in Panel I.}} \]