Question

If the geometric solid blocks shown below are cut along a single flat plane, which of these can have the cross-section of a regular hexagon (all sides equal)? Assume all blocks are extruded from polygons with sides of equal length.

• A. A
• B. B
• C. C
• D. D

Hint:

For cross-section questions, visualize slicing parallel to the base: prisms preserve the polygonal shape, while cubes can form hexagons only with special diagonal cuts.

Answer 1

The Correct Option is D

Step 1: Recall geometric property.
A regular hexagon can appear as a cross-section of a cube (under a diagonal cut) or a regular hexagonal prism.
Step 2: Analyze shapes.
- (A): Square prism → can give square or rectangle, not a hexagon.
- (B): Cuboid → only rectangles/squares.
- (C): Irregular extrusion → cannot yield a regular hexagon.
- (D): Hexagonal prism → cross-section by a plane parallel to base gives a perfect hexagon. With a proper diagonal cut, it yields a regular hexagon.
Step 3: Conclude.
Thus, only option (D) gives a regular hexagonal cross-section. Final Answer: \[ \boxed{\text{D}} \]