Choose the box that is similar to the box formed from the given sheet of paper…

2025

Choose the box that is similar to the box formed from the given sheet of paper (X).

  1. A.

    1 only

  2. B.

    1, 2 and 3 only

  3. C.

    2 and 3 only

  4. D.

    1, 2, 3 and 4

Attempted by 1 students.

Show answer & explanation

Correct answer: D

Concept: When a flat sheet is folded into a cube, its six squares pair up into exactly three pairs of OPPOSITE faces. Two faces that are opposite can never both be seen in the same view of the cube; any two faces that are NOT opposite are automatically ADJACENT and can appear together. In any straight run of three squares within the net, the two end squares always fold to become an opposite pair, while the middle square becomes a face adjoining both of them.

Application:

  1. The bottom row of sheet (X) is a straight run of three squares - dot, '+', blank. By the straight-run rule, the two end squares are opposite: the dot square is opposite this blank square, and the '+' square (the middle one) is adjacent to both.

  2. The top row of sheet (X) is also a straight run of three squares - circle, blank, blank - attached to the bottom row through the shared middle blank square. By the same rule, the circle square is opposite the last blank square in this row, and the middle blank square is adjacent to both.

  3. A cube has only three pairs of opposite faces in total. Two pairs are already fixed above (dot opposite blank, circle opposite blank); the two faces left over - the '+' square and the remaining blank square - must therefore form the third opposite pair.

So none of the three marked faces (dot, '+', circle) is opposite another marked face - each one is opposite a blank face instead. That means dot, '+', and circle are mutually adjacent on the cube and can appear together, in any combination, in a corner view.

Cross-check:

  • Figure (1) shows only the '+' face with two blank faces - none of these three is an opposite pair, so this fold is valid.

  • Figure (2) shows the '+' face together with the dot face (plus a blank) - dot and '+' are adjacent, not opposite, so this fold is valid.

  • Figure (3) shows the circle face together with the dot face (plus a blank) - circle and dot are adjacent, not opposite, so this fold is valid.

  • Figure (4) shows the dot face together with the circle face (plus a blank) - again adjacent, not opposite, so this fold is valid.

Since every figure only ever pairs faces that are adjacent (never the true opposite partners), all four cubes - figures (1), (2), (3) and (4) - can be formed by folding sheet (X), matching the option '1, 2, 3 and 4'.

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