The paper as showin the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?
Note: The figures showin are representative.
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Answer: A
To determine which of the 3D cube options correctly represents the folded paper net, we can use the Rule of Opposite Faces.
1. Identifying Opposite Pairs from the Net
In a standard cube net:
- Alternate faces in a straight line of four squares are opposite to each other.
- The two side flaps (projecting out from the main column) fold to become opposite to each other.
Based on the given net, the opposite pairs are:
- Pair 1: The face with the triangle and the face with the cross (X) are opposite to each other.
- Pair 2: The face with the white circle (with a central dot) and the face with the solid black circle are opposite to each other.
- Pair 3: The face with the diagonal line / square pattern and the face with the shaded square are opposite to each other.
2. Eliminating Invalid Options
Opposite faces can never share an edge and therefore cannot be visible at the same time in any 3D view of the cube.
- Option B: Shows both the triangle and the cross adjacent to each other. Since these are opposite faces, this is incorrect.
- Option C: Shows both the white circle with a dot and the solid black circle adjacent to each other. Since these are opposite faces, this is incorrect.
- Option D: Shows both the diagonal pattern and the shaded square adjacent to each other. Since these are opposite faces, this is incorrect.
Thus, Option A is the only representation where no two opposite faces are adjacent to each other, making it the correct folded cube.
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