Question: Choose the box that is similar to the box formed from the given…

2025

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

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

Attempted by 1 students.

Show answer & explanation

Correct answer: D

Concept: In a 'which cube can be formed from this sheet' question, first read off from the net (X) which two faces are opposite each other and which pattern repeats. A folded cube can only show, at any single corner, faces that genuinely sit adjacent to one another once the sheet is folded - so a candidate cube is wrong the instant it puts a stated opposite pair side by side, displays a face pattern the sheet never contains, or crowds more copies of a repeating pattern at one corner than the sheet allows.

Application: Sheet (X) is a cross of four blank arm-squares (top, bottom, left, right) around a centre square bearing a circle - only five squares, one short of a cube's six faces. Each arm-square also carries a small triangular flap beyond its outer edge (the left and right flaps solid black, the top and bottom flaps blank); folding (X) brings these four flaps together to close up the sixth face, giving it a black-cornered, white-bowtie pattern, and this assembled face lands directly opposite the circle face. Among the four blank arm-squares themselves, top-bottom form one opposite pair and left-right form the other, so no three of them can ever be mutually adjacent. Checking each option against these two facts:

  • (1) is invalid - one visible face is a single black diagonal triangle; sheet (X) only ever produces blank faces, the circle face, and the black-cornered bowtie face, and none of those is a plain single diagonal triangle.

  • (2) is invalid - it shows three blank faces meeting at one corner, which sheet (X)'s two opposite blank pairs can never produce.

  • (3) is invalid - it places the circle face and the bowtie face next to each other at one corner, but folding (X) puts them directly opposite each other, so they can never be adjacent.

  • (4) satisfies both facts - the circle and bowtie faces never touch, and no three blank faces are forced together.

Cross-check: Re-applying the two rules to figure (4) confirms every visible corner is consistent with how sheet (X) folds, and no other option clears both checks - so (4) is the cube formed from (X).

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