In a machining operation, if a cutting tool traces the workpiece such that the directrix is perpendicular to the plane of the generatrix as shown in figure, the surface generated is

The correct option is cylindrical.

In machining and geometric modeling, physical surfaces are created through the relative motion of a cutting tool and a workpiece. This generation of surfaces is described by two key geometric elements:
1. Generatrix: The generator line or curve that represents the shape of the cutting profile.
2. Directrix: The directress line or path along which the generatrix moves to sweep out the surface.

As shown in the provided figure, the label Generatrix points to a closed loop (a circle or ellipse viewed in perspective) representing the profile of the workpiece. The label Directrix points to a straight line perpendicular to the plane of the closed loop, along which the generatrix moves (indicated by the horizontal arrow).

When a closed planar curve (the generatrix) is translated along a straight line (the directrix) that is perpendicular to the plane of the curve, it sweeps out a uniform, column-like geometry. By definition, a surface generated by translating a curve along a straight line path is a cylindrical surface. Hence, the surface generated in this operation is cylindrical.