Steel shafts are finished on a lathe with a carbide tool with a cutting edge angle of $90\backslash$deg $.$ The nose radius is $0\mathrm{.}2$

mm$.$ The feed is $0\mathrm{.}1$ mm per revolution.

a$.$ Calculate the transverse roughness of the turned surface. $(2$ points$)$

b$.$ Explain how your calculation is structured by means of a sketch. $(2$ points$)$

c$.$ In addition, what factors influence the surface quality of the turned surface? $(2$ points$)$