Difficulty: Medium
Correct Answer: Correct
Explanation:
Introduction / Context:
In descriptive geometry and sheet-metal pattern making, a key distinction exists between developable and non-developable surfaces. Developable surfaces (cylinders, cones) can be flattened without stretching; warped or double-curved surfaces (e.g., spheres, saddles) cannot be flattened without distortion.
Given Data / Assumptions:
Concept / Approach:
A surface that is double-curved requires metric distortion to lie flat. Practical workflows approximate such surfaces with patches or segmented panels, but a single, exact unrolled pattern is mathematically impossible without stretching.
Step-by-Step Solution:
1) Classify the surface: cylindrical/conical (developable) vs spherical/saddle (non-developable).2) If double-curved, anticipate distortion when forced flat.3) Use tessellation or approximate panelization for fabrication.4) Validate fit via templates or digital unfolding with allowed strain.
Verification / Alternative check:
Attempting true-length development in CAD for a sphere will fail unless elastic deformation (strain) is permitted, confirming non-developability.
Why Other Options Are Wrong:
Surface area magnitude is irrelevant; adding seams enables approximation, not perfect development; scaling does not change intrinsic curvature.
Common Pitfalls:
Assuming any 3D surface can be developed; ignoring allowable strain limits; underestimating the need for pattern segmentation.
Final Answer:
Correct
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