How many dots lie opposite to the face having three dots, when the given…
2023
How many dots lie opposite to the face having three dots, when the given figure is folded to form a cube?
- A.
2
- B.
4
- C.
5
- D.
6
Attempted by 1 students.
Show answer & explanation
Correct answer: D
When a two-dimensional net is folded into a cube, each square becomes one face of the cube. The standard rule for locating opposite faces is: in every straight, unbroken run of three consecutive squares in the net (a row or a column with no bend), the two squares at the ends of that run always fold into a pair of opposite faces of the cube, because the square between them becomes one of the four side faces standing between the two end faces.
This net is made of exactly two such straight runs of three squares, joined to each other along one shared edge (the three-dot square and the four-dot square sit side by side there):
Straight run of three squares in the net | Squares at the two ends of the run | Opposite pair formed on the cube |
|---|---|---|
Six-dot face, One-dot face, Three-dot face (in that order) | Six-dot face and Three-dot face | Six-dot face is opposite the Three-dot face |
Four-dot face, Two-dot face, Five-dot face (in that order) | Four-dot face and Five-dot face | Four-dot face is opposite the Five-dot face |
Cross-check: a cube always has exactly three pairs of opposite faces. The straight-run rule above already fixes two of the three pairs (Six-dot opposite Three-dot, and Four-dot opposite Five-dot); the two faces left over -- the One-dot face and the Two-dot face -- are automatically forced into the third and last pair, which matches an independent fold-through check of the net. Therefore, the face bearing three dots is opposite the face bearing six dots -- the answer is 6 dots.