Question

X1 is a 3D form generated from the shape X, using certain 3D operations. It has 11 surfaces in total. If the same operations are carried out on shape Y, how many surfaces would the resulting 3D form have?

Hint:

For such 3D reasoning questions: surfaces = (number of edges/faces in base 2D figure) × (effect of extrusion). Compare with given X → X1 relation.

Answer 1

Step 1: Understand given transformation.
- Shape X (2D) when extruded + modified gave X1 (3D).
- Resulting solid X1 has 11 surfaces.
Step 2: Relating surfaces.
- Shape X is a quadrilateral-like figure.
- Shape Y is more complex: a composite with a circle + rectangle + triangle.
- The same operation that generated 11 surfaces for X will proportionally increase the number of surfaces for Y.
Step 3: Count components in Y.
- Y has 6 boundary edges in its 2D form (circle arc, straight edges).
- When extruded and modified in the same way, the 3D solid will yield 22 surfaces.
Final Answer: \[ \boxed{22 \, \text{surfaces}} \]