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
Fold the net one face at a time and track which shaded faces end up adjacent versus opposite.
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 isB
Solution and Explanation
Step 1: Number the faces of the net.
Label each panel of the flat net in Panel I in the order they would land as the paper is folded, and mark which of them carry the shaded pattern.
Step 2: Fold the net face by face.
Fold along each dashed line one at a time, keeping track of which face becomes the top, the bottom and the four sides, and note which shaded faces end up sharing an edge versus ending up on opposite faces of the cube.
Step 3: Compare against cube (i) and cube (ii).
Cube (i) shows two shaded faces meeting at an edge where the net actually places them on opposite faces, so cube (i) contradicts the fold. Cube (ii) shows the shaded faces sharing an edge exactly where the folded net says they should, and no shaded face is misplaced.
Final Answer:
Tracing the fold rules out cube (i) and confirms cube (ii), so only cube (ii) can come from the net in Panel I.
\[ \boxed{\text{Only (ii)}} \]
