In solid geometry, is it correct that a solid body is bounded by the surfaces that enclose its volume (e.g., planes, cylinders, spheres forming the outer boundary)?
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ACorrect
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BIncorrect
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COnly true for prisms
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DOnly if surfaces are planar
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EOnly true in orthographic view
Answer
Correct Answer: Correct
Explanation
Introduction / Context:Basic definitions anchor all higher-level modeling and drafting work. A solid occupies volume; its boundary is a closed set of surfaces. Recognizing this helps in feature operations (shell, fillet), sectioning, and mass property evaluation in CAD.
Given Data / Assumptions:
- Solids are 3D regions with interior volume.
- Bounding surfaces may be planar or curved.
- The boundary is closed (no gaps) to enclose volume.
Concept / Approach:The definition of a solid includes an external boundary forming a manifold surface. Whether piecewise planar (polyhedra) or smoothly curved (spheres), the enclosing surfaces separate interior from exterior, enabling volume, centroid, and inertia calculations.
Step-by-Step Solution:
Identify the body: any 3D object with volume (e.g., cube, cylinder).List its enclosing faces/surfaces: planes, cylindrical, or spherical patches.Confirm closure: surfaces join edge-to-edge without gaps.Conclude: the solid is indeed bounded by its enclosing surfaces.Verification / Alternative check:In CAD, viewing section cuts shows a finite interior. Mass properties require a watertight boundary, reinforcing the definition.
Why Other Options Are Wrong:Limiting truth to prisms or planar faces ignores curved solids; projection/view choice does not affect geometric definition.
Common Pitfalls:Confusing wireframe (no surface) with solids; mistaking open surfaces (no volume) for solids.
Final Answer:Correct