Question

The figure shows the top view, front view, and side view of a 3D solid. What is the minimum number of surfaces that a solid with these views can have? Assume no hidden lines. 

• A. 12
• B. 14
• C. 16
• D. 30

Hint:

For 3D orthographic view puzzles, look for a solid that produces identical projections (circle in square from all directions). This usually means a cylinder in a cube or a solid with 16 surfaces.

Answer 1

The Correct Option is C

Step 1: Interpret the projections.
- Top view: A square enclosing a circle.
- Front view: A square enclosing a circle.
- Side view: A square enclosing a circle.
This indicates the solid is a cylinder inscribed in a cube.
Step 2: Consider the solid’s surfaces.
If the object has a cylindrical portion cut inside a cube, then:
- The cube contributes 6 flat square surfaces.
- The cylinder contributes 2 circular surfaces (top and bottom).
- Additionally, the intersection between cube and cylinder produces several curved + flat facets when approximated as a polyhedral solid.
Step 3: Known minimum solid.
The minimum polyhedral solid that can give all three views (circle inside square) is the cylinder approximated with a polygonal base. The smallest polygon approximation consistent with the projections leads to 16 surfaces. Final Answer: \[ \boxed{16} \]