The drawing below shows a closed box made out of cardboard. Next to it are three unfolded (developed) views of the same cardboard box. Two of these options are correct. Select the wrong one by marking X in the box provided below.
Show Hint
To spot the wrong unfolded view, focus on how the faces of the closed box are connected. Pay close attention to:
Opposite faces: In a cube or box, opposite faces never share an edge in the unfolded (net) view.
Adjacent faces: Only adjacent faces in the 3D box can be directly connected in the net.
Face orientation: Check that when folded, the faces align properly without overlapping or being misoriented.
Reasoning To determine the correct unfolded net corresponding to the given Z-shaped box, one must mentally fold the net back into its three-dimensional form and verify if all faces align properly without overlaps or gaps. Correct Nets The first and second unfolded nets provided can both be folded in such a way that they accurately form the Z-shaped box. This is because: The arrangement of the faces allows the appropriate 90-degree folds. The alternating long and short flaps correspond correctly to the geometry of the box. All edges align perfectly to enclose the box completely. Incorrect Net (Third Option) The third net is incorrect due to the following reasons: Misalignment of Faces: When designating the largest central face as the base, folding up the adjacent faces reveals that the narrow end pieces on the right side do not align correctly. Orientation Problem: The faces on the right end of the third net are mirrored or positioned improperly. This results in the flaps being unable to meet properly at the edges, preventing the net from folding into the intended Z-shape. Flap Arrangement: The Z-shaped box requires an alternating pattern of long and short flaps that bend at right angles. The third net fails to reproduce this pattern because the faces on the right are flipped or reversed, disrupting the fold sequence. Conclusion Because the third unfolded net cannot be folded to form the Z-shaped box correctly, it is the incorrect choice. The first and second nets, by contrast, maintain the proper arrangement and orientation of faces, confirming their validity as correct nets of the box. Therefore, the selection of the third net as the incorrect unfolded view is justified.
