Question

using the piling method, which of the following can be constructed from polygons alone or discs alone?

check all that apply.

a. pyramid (including the vertex)
b. cylinder
c. prism
d. cone (including the vertex)
e. cone (not including the vertex)
f. cube

Explanation:

Analyze the piling method concept

The piling method constructs 3D solids by stacking (piling) 2D cross-sections (polygons or discs) of varying or constant sizes.

• A pyramid (including the vertex) requires stacking similar polygons that scale down to a single point (the vertex, which is a point, not a polygon). Thus, it cannot be constructed from polygons alone because the vertex is a point.
• A cylinder is constructed by stacking identical discs. This uses discs alone.
• A prism is constructed by stacking identical polygons. This uses polygons alone.
• A cone (including the vertex) requires stacking discs that scale down to a single point (the vertex, which is a point, not a disc). Thus, it cannot be constructed from discs alone.
• A cone (not including the vertex) is constructed by stacking discs of decreasing radii, excluding the limiting point. This uses discs alone.
• A cube is a specific type of prism constructed by stacking identical squares. This uses polygons alone.

Determine the valid options

Based on the definitions:

• B (Cylinder): Discs alone.
• C (Prism): Polygons alone.
• E (Cone, not including the vertex): Discs alone.
• F (Cube): Polygons alone.

Answer:

• A. Pyramid (including the vertex)
• B. Cylinder (Correct answer)
• C. Prism (Correct answer)
• D. Cone (including the vertex)
• E. Cone (not including the vertex) (Correct answer)
• F. Cube (Correct answer)