Question

Identify the combination of solids which is an example of combination of polyhedron.

• A. Figure A
• B. Figure B
• C. Figure C
• D. Figure D

Hint:

If a solid has any curved lateral surface (such as a cylinder, cone, or sphere), it cannot be classified as a polyhedron. Prisms, pyramids, and the five Platonic solids are all polyhedrons.

Answer 1

The Correct Option is B

Step 1: Definition of a Polyhedron:
A polyhedron is a 3-dimensional solid bounded entirely by flat polygonal faces (such as triangles, squares, pentagons, hexagons, etc.). Prisms and pyramids are prime examples of polyhedrons.

Step 2: Definition of Solids of Revolution:
Solids that possess curved, rounded surfaces generated by revolving a shape about an axis (such as cylinders, cones, and spheres) are categorized as curved solids or solids of revolution. They are not polyhedrons.

Step 3: Analyzing the Options:

• Option (A): Both the cylinder and hemisphere are solids of revolution. (Not a combination of polyhedrons).
• Option (B): A pentagonal prism and a hexagonal prism are both bounded entirely by flat, straight-edged polygonal surfaces. Hence, both are polyhedrons. This represents a pure combination of polyhedrons.
• Option (C): A square pyramid is a polyhedron, but a cylinder is a solid of revolution.
• Option (D): A hexagonal prism is a polyhedron, but a cylinder is a solid of revolution.

Step 4: Conclusion:
Therefore, option (B) is the only correct answer.