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 the given alternatives (1), (2), (3) and (4), the boxes that are similar to the box that will be formed.
Choose the box that is similar to the box formed from the given sheet of paper (X).
- A.
1 and 3 only
- B.
2 and 4 only
- C.
3 and 4 only
- D.
1 and 4 only
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: When a flat net is folded into a closed box, every face pairs with exactly one face directly opposite it on the box. Two faces that sit two squares apart along a straight run in the net, or one square attached above and one attached below the same shared square, always end up opposite each other once folded - never side by side. So in any valid three-face corner view of the folded box, two genuinely opposite faces can never be shown touching each other; a picture that shows them adjacent cannot be a real fold of that net.
Application: Tracing sheet (X), the four faces running along the middle row wrap around the box to form its four side faces, giving two white rectangular faces opposite each other and two shaded (black) rectangular faces opposite each other. The square face attached above this row and the square face attached below it become the top and bottom of the box, giving one white square face opposite one shaded square face. So the two shaded RECTANGULAR faces are opposite one another and can never appear touching in a valid view, while a shaded square face is free to sit beside either shaded rectangular face, since those pairs are genuinely adjacent on the box.
Cross-check - examining each figure:
Figure (1): the two shaded faces visible are a shaded square face beside a shaded rectangular face - a genuinely adjacent pair on the box, so this is a valid fold of sheet (X).
Figure (2): the two visible side faces are both shaded rectangular faces sitting directly next to each other - impossible, since those two faces are opposite each other on the box.
Figure (3): only one face is shaded, touching two unshaded faces - no opposite-pair conflict, so this is a valid fold of sheet (X).
Figure (4): all three visible faces are shaded, which forces two shaded rectangular faces to sit next to each other - impossible for the same reason as figure (2).
So only the boxes in figures (1) and (3) can be formed by folding sheet (X).