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
Track the diamond-shaded face first, since it appears in the same position on both candidate cubes. Then check whether the triangle-shaded faces around it keep the same corner touching the same fold line as in the flat net; a fold can never flip a shaded triangle to the other side of its diagonal.
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
Step 1: Find the face that anchors the comparison.
The diamond-shaded square in the net is the most distinctive shape, so track it first. It sits in the middle of the vertical strip, with one square above it and two squares below it joined at its bottom edge. Once folded, this face becomes the cube's front face in both candidate cubes (i) and (ii), since both show the diamond in the same central position.
Step 2: Use the shared edge, shared corner rule.
When two faces are joined by a fold line in the flat net, the corner of any shaded triangle that touches that fold line must still touch the matching edge once the cube is assembled, since folding never moves a shaded corner away from the edge it was drawn against. This is a quick check for these paper-folding questions.
Step 3: Apply the rule to the top face.
The square directly above the diamond carries a small square patch, and the row above that carries the triangle and the fully shaded square. Tracing the fold, the triangle's shaded corner sits against the same edge that borders the diamond's face. In cube (i), the top face's triangle touches the front-top edge at that exact corner. In cube (ii), the triangle on the top face is shaded on the other side of its diagonal, so its corner touches a different edge instead. That breaks the shared-edge rule for cube (ii).
Step 4: Apply the rule to the side face.
The bottom row's second square carries a small triangle near one corner, folded so it lands on the face beside the diamond. Cube (i) keeps this triangle at the corner the rule predicts; cube (ii) does not show the same match, confirming the mismatch shows up on more than one face.
Step 5: Rule out the remaining options.
Since cube (i) passes the shared-edge check on every face while cube (ii) fails it, the option claiming both cubes work is wrong, and so is the option claiming neither cube works.
Final Answer:
Only cube (i) keeps every shaded corner on the edge the net demands, so the net folds into cube (i) alone.
\[ \boxed{\text{Option (A)}} \]
