In geometry and technical sketching, is a sphere correctly described as a double-curved body that can be generated by revolving a circle about one of its diameters?

Introduction / Context:
A sphere is a fundamental 3D geometric form encountered across drafting, CAD, and manufacturing. Understanding how standard solids are generated (revolve, extrude, sweep) is essential for both manual sketching and parametric modeling. This item checks whether the learner recognizes the classical generative definition of a sphere.

Given Data / Assumptions:

• A sphere has continuous double curvature (no flat faces or edges).
• Generating methods such as revolve are admissible conceptual tools.
• The circle used for revolution is planar and has a defined diameter/axis.

Concept / Approach:
In constructive geometry, a sphere can be generated by revolving a circle 360 degrees about any of its diameters. Each point on the circle traces a circle in space about the axis, producing a set of circles whose union forms the spherical surface. This matches the definition of constant-radius points from a center.

Step-by-Step Solution:

Verification / Alternative check:
Equivalently, a sphere is the locus of points equidistant from a center. The revolve construction produces precisely that locus. CAD systems (REvolve) and descriptive geometry texts confirm equivalence.

Why Other Options Are Wrong:
“Incorrect”: contradicts standard geometry. “Only true for hemispheres,” “True only in perspective drawings,” and “True only for great circles” add constraints that do not exist in the definition or construction.

Common Pitfalls:
Confusing the revolve axis (a diameter) with an external axis; mixing up sphere with torus (circle revolved about an external axis).

Final Answer:
Correct