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It called the curved surface area. There is no special name for it.
what is the name of a smooth curved line around the outside of a regular polygon
Sphere, ellipsoid, torus, paraboloid, hyperboloid are shapes with only curved surfaces. Hemisphere, quadrant, cone and cylinder are examples of shapes with curved and plane surfaces. There are, of course, many others.
An ellipse is the proper name for an oval shape, however, a circle is a closed curved shape similar to an oval shape.
The mathematical name is a sector.