The sheet of paper shown in the figure (X) given on the left hand side, in…
2025
The sheet of paper shown in the figure (X) given on the left hand side, in each problem, is folded to form a box.Choose from amongst the alternatives (1), (2), (3) and (4), the boxes that are similar to the box that will be formed.
- A.
1 and 2 only
- B.
2 and 3 only
- C.
2 and 4 only
- D.
1, 2, 3 and 4
Attempted by 465 students.
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Correct answer: D
Answer: Figures 1, 2, 3 and 4.
Reason: Use the opposite-face and adjacency relationships produced by the net to check each cube.
Two half-shaded faces become opposite each other when the net is folded.
The face with the dot becomes opposite one of the blank faces (not adjacent to the other blank faces that lie around it).
Any candidate cube that preserves these opposite-face relations and the shown adjacencies can be formed from the net.
Figure 1: The half-shaded face shown on top is opposite the other half-shaded face and the dotted face is positioned relative to blank faces exactly as on the net, so it matches.
Figure 2: The arrangement preserves the two opposite half-shaded faces and the dotted face opposite a blank face, so it matches.
Figure 3: The half-shaded faces are opposite and the dotted face is opposite a blank face as required, so it matches.
Figure 4: This figure also satisfies the opposite-face relations from the net, so it matches as well.
Conclusion: All four given cubes (1), (2), (3) and (4) can be formed from the net. Therefore the correct choice is the set containing all four figures.