Descriptive Geometry — Warped (double-curved) surfaces are not developable; they cannot be unrolled or unfolded to a plane without distortion, unlike cylinders or cones which are developable.

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:

  • Warped surfaces have curvature in two principal directions.
  • Flattening to a plane is attempted without stretching or tearing.
  • Developable surfaces have zero Gaussian curvature; warped ones do not.


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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