Solids of revolution — egg-shaped forms Which solid is generated by revolving an ellipse about one of its principal axes, producing an egg-like (spheroidal) shape used in product and aerodynamic design?

Introduction / Context:Many engineering shapes are created as solids of revolution due to manufacturing practicality and favorable structural/aerodynamic properties. Revolving conic sections yields common primitives used in modeling and analysis.

Given Data / Assumptions:

• The curve is an ellipse.
• The operation is revolution about one of the ellipse’s axes.
• The result is described as egg-shaped or spheroidal.

Concept / Approach:Revolving an ellipse about its major or minor axis yields an ellipsoid (specifically, a prolate or oblate spheroid). This form appears in pressure vessels, lenses, and streamlined bodies.

Step-by-Step Solution:Identify the base curve: ellipse.Recognize that revolving an ellipse does not produce a torus (circle around an external axis), cone (triangle around an edge), or cylinder (rectangle around a side).Conclude the correct solid is an ellipsoid.

Verification / Alternative check:CAD systems label this feature “revolve” of an ellipse to create a spheroid/ellipsoid. Mathematical definitions align with surfaces of constant sum of distances to two foci.

Why Other Options Are Wrong:

• Torus: generated by revolving a circle about an axis offset from the circle.
• Cone: generated by revolving a right triangle.
• Cylinder: generated by revolving a rectangle about one side.

Common Pitfalls:Calling all egg-like bodies “spheres”—a sphere is a special ellipsoid with equal axes.

Final Answer:Ellipsoid