Question

Consider a 3D hollow geometry with six faces and nine equal edges, as indicated in Figure D. Which of the given shapes will generate the described 3D geometry when folded along the dotted lines?

• A. Only \( P \)
• B. \( Q \) and \( R \)
• C. \( P, Q, \) and \( R \)
• D. Only \( S \)

Hint:

To determine if a net forms a 3D shape, check the number of faces and how the edges connect. Folding along the dotted lines mentally can help visualize the final structure.

Answer 1

The Correct Option is C

Step 1: Analyze the given 3D hollow geometry (Figure D). It consists of six triangular faces and nine equal edges, forming a symmetrical structure.

Step 2: Identify which given net diagrams (P, Q, R, S) can be folded along the dotted lines to form the described 3D shape.
- Option P: Contains six triangles arranged in a way that they can be folded into a symmetrical 3D figure.
- Option Q: Also consists of six triangles correctly placed for forming the shape.
- Option R: Maintains the same triangular face count and edge arrangement, making it valid.
- Option S: The triangular faces are not arranged correctly to form the required 3D structure.

Step 3: Since P, Q, and R can be folded into the required 3D shape, the correct answer is:
\[ \text{P, Q, and R} \] Thus, the correct answer is option C.