The paper as shown in the figure is folded to make a cube where each square corresponds to the a particular face of the cube. Which one of the following options correctly represents cube?

Note: The figures shown are representative.

Correct Answer: The option showing the cube with a filled circle on the top face, an upward-pointing triangle outline on the front face, and a blank face on the right side (represented by the first option image).

Step-by-Step Explanation:

1. Analyze the Net of the Cube
By analyzing the unfolded paper (the cube net) shown in the first image, we can identify the pattern on each of the six faces:

• Top flap: Filled Circle
• Middle horizontal row (from left to right):
  • Face 1: Blank Face
  • Face 2: Triangle Outline (pointing upwards)
  • Face 3: Blank Face
  • Face 4: Filled Triangle (pointing upwards)
• Bottom flap: Circle Outline

2. Determine the Opposite Pairs of Faces
In a standard cube net, faces that are separated by exactly one square fold to become opposite to each other. Opposite faces can never be adjacent and thus can never be visible at the same time in any 3D view of the cube.
Let's pair the opposite faces based on the net:

• Pair 1: The Top flap and Bottom flap are opposite.
  ��� Filled Circle is opposite to Circle Outline.
• Pair 2: Alternating faces in the horizontal row are opposite.
  ⇒ Blank Face 1 (Face 1) is opposite to Blank Face 2 (Face 3).
• Pair 3: The remaining alternating faces in the horizontal row are opposite.
  ⇒ Triangle Outline (Face 2) is opposite to Filled Triangle (Face 4).

3. Analyze the Side-by-Side Adjacency Rules
From the opposite pairs established above, we can derive the following rules for any valid 3D representation of the folded cube:
• Rule A: The Filled Circle and Circle Outline cannot be visible at the same time.
• Rule B: The Triangle Outline and Filled Triangle cannot be visible at the same time.
• Rule C: Since the only two blank faces on the cube are opposite to each other, a valid view can show at most one blank face. Any option showing two blank faces at the same time (such as the third option image, which shows a top blank face and a right blank face) is invalid.

4. Verify the Correct Option
The correct cube shows:
• Top Face: Filled Circle (from Pair 1)
• Front Face: Triangle Outline (from Pair 3)
• Right Face: Blank Face (from Pair 2)
Since these three faces belong to three different opposite pairs, they do not violate any opposite-face rules and are mutually adjacent. Additionally, folding the top flap (Filled Circle) back and the right flap (Blank) back aligns perfectly with the upward orientation of the front Triangle Outline. Thus, this option represents the correctly folded cube.