Taper turning produces a conical surface. A taper is a workpiece whose diameter changes uniformly along its axis, so its outer surface forms part of a cone — hence "conical" is the correct description.

The geometry arises from how the tool moves relative to the rotating job. In ordinary (straight) turning the tool feeds strictly parallel to the work axis, holding the diameter constant. In taper turning the tool path is deliberately inclined to the axis, so as it travels along the length the depth of cut, and therefore the diameter, changes at a steady rate. The half-cone angle is set by the tangent relationship tan α = (D − d) / (2L), where D and d are the large and small diameters and L is the taper length.

Common methods of generating a taper on a centre lathe include:

• Compound rest (swivel) method — the top slide is swivelled to the required angle; suited to short, steep tapers.
• Tailstock set-over (offset) method — the tailstock is shifted laterally; used for long, gentle tapers on work held between centres.
• Taper turning attachment — a guide bar steers the cross-slide; gives accurate, repeatable tapers.
• Form tool method — a wide angled tool reproduces very short tapers.

The other options describe surfaces made by different operations, not taper turning: a cylindrical surface comes from plain straight turning (constant diameter), a flat surface is produced by a facing operation across the end, and a curved (contoured) surface results from form turning or profile turning. None of these matches the uniformly tapering shape, so conical is correct.