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 (A).
(A)
- A.
Option 1,2 and 3
- B.
Option 1,3 and 4
- C.
Option 2 and 3
- D.
Option 2,3 and 4
Show answer & explanation
Correct answer: B
Concept: When a two-dimensional net is folded into a cube, two faces of the net are opposite each other if exactly one square lies between them along a straight row or column of the net. Faces that are adjacent in the net stay adjacent (share an edge) on the folded cube, so two faces that are opposite in the net can never sit side by side on the assembled cube.
Application: Folding the given sheet (A), one of its faces takes the form shown below:
This face is opposite the face bearing a square.
One blank face is opposite the other blank face.
The remaining blank face is opposite the face bearing the '=' sign.
Since only one pair of blank faces can sit opposite each other, at most two blank faces can ever be mutually adjacent on a valid cube - a fold that shows three blank faces meeting at a single corner cannot be formed from this sheet.
Checking each candidate cube against these opposite-face pairs:
Candidate cube | Verdict | Reason |
|---|---|---|
(1) | Valid | Its visible adjacent faces match the derived opposite-face pairs. |
(2) | Not valid | Three blank faces meet at one corner, which the derived pairing forbids. |
(3) | Valid | Its visible adjacent faces match the derived opposite-face pairs. |
(4) | Valid | Its visible adjacent faces match the derived opposite-face pairs. |
Cross-check: cube (2) is the only candidate that violates a derived opposite-face pair; cubes (1), (3), and (4) show no such violation. So exactly cubes (1), (3), and (4) can be formed from the given sheet - matching 'Option 1,3 and 4'.