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
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The Correct Option isA
Solution and Explanation
Step 1: Label the six faces of the net.
Panel I is a strip of six unit squares joined by the marked dashed fold lines: the top row has a square with a triangle shaded in its lower-left corner (face 1) joined to a fully shaded square (face 2); hanging from that seam is a smaller square carrying a small grey square patch (face 3); below face 3 sits a square with a large shaded diamond (face 4); and the bottom row has a square with a large triangle shaded from its top-left to bottom-right corner (face 5) joined to a square with a small triangle shaded near its bottom-right corner (face 6).
Step 2: Work out which faces sit next to which once folded.
Each dashed line is a hinge, so folding brings every pair of squares joined by a dashed line onto two faces of the cube that share an edge. Face 4, the diamond, sits between face 3 above it and faces 5 and 6 below it, so once folded, the diamond face becomes the front face of the cube, and the triangle patterns on faces 1, 2, 5 and 6 land on the faces that surround it, each keeping the same corner of its shaded triangle touching the same shared edge it touched in the flat net.
Step 3: Check cube (i) against this layout.
In cube (i), the diamond sits on the front face exactly as face 4 predicts. The triangle on the top face meets the front-top edge at the same corner that face 1's triangle meets the face 1 to face 4 fold line in the net, and the sliver of shading on the right face lines up with face 6's small triangle at the same shared corner. Every shaded region keeps the corner and edge contact it had in the flat net, so cube (i) is a genuine folding of Panel I.
Step 4: Check cube (ii) against this layout.
In cube (ii), the diamond again sits correctly on the front face, but the triangle on the top face is shaded on the opposite side of its diagonal compared with face 1 in the net. A simple fold along a shared edge cannot flip a triangle to the other side of its own diagonal while keeping the diamond fixed, so this cube changes the shape that should appear on the top face. That mismatch rules out cube (ii).
Step 5: Decide between the four options.
Since cube (i) reproduces every face of Panel I correctly and cube (ii) does not, the option that both cubes work and the option that neither works are both ruled out.
Final Answer:
Only cube (i) matches a genuine folding of the net in Panel I, so option (A) is correct.
\[ \boxed{\text{Option (A): Only (i)}} \]
