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 the cubes shown in Panel II, which one of the options is correct? (Panel I shows a flat cross-shaped net of six squares: a vertical strip of four squares one above another, with one extra square attached to the left of the second square in that strip and another extra square attached to its right, all joined along dashed fold lines. Some squares carry grey shaded regions and some are left plain white. Panel II shows two separate solid cubes, labelled (i) and (ii), each with grey shaded regions on some of their visible faces.)
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Trace which net squares become which cube faces (front, back, top, bottom, left, right) and check that shaded neighbors stay adjacent in the same orientation after folding.
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.
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The Correct Option isB
Solution and Explanation
Step 1: Understanding the Question.
We are given a flat net of six squares (Panel I) that folds up into a cube, with certain regions shaded grey. We must decide which of the two solid cubes drawn in Panel II, (i) or (ii), could actually be the folded result, based on where the grey regions land and how they sit next to each other.
Step 2: Key Approach.
Label one square of the net as the front face, since it stays fixed while the rest fold around it. The squares directly above, below, left, and right of the front face become the top, bottom, left, and right faces of the cube, and the square at the far end of the strip becomes the back face, opposite the front.
Once every square is assigned to a face of the cube, two facts must both be checked in each candidate cube: which faces carry the grey shading, and how the shaded region on one face lines up with the shaded region on its neighboring face along the edge they share, since folding fixes both the position and the rotation of every face at once.
Step 3: Detailed Explanation.
Assigning the net's six squares this way shows that the fully grey square becomes the back face, the square with the grey triangular corner becomes the top face, the mostly grey square with the white notch becomes the left face, and the square with the small grey corner patch becomes the right face, while the front and bottom faces stay plain white.
Because folding is rigid, the grey triangle on the top face and the grey patch on the right face must meet the shared top-right edge of the cube in one specific relative rotation, and the same is true for every other pair of neighboring shaded faces.
Checking cube (i): the grey regions shown on its visible faces meet each other at the wrong edge and in the wrong relative rotation compared to what the net requires, so cube (i) cannot be the folded result of this net.
Checking cube (ii): the grey regions shown on its visible faces meet at the same edges and in the same relative rotation that folding the net produces, so cube (ii) is consistent with the net.
Step 4: Final Answer.
Since only cube (ii) keeps the shaded faces in the positions and orientations that folding Panel I actually produces, only (ii) can correspond to the unfolded cube in Panel I.
