$(20$ points$)($a$)5$ points$$Label each region in the isothermal transformation diagram of hypoeutectoid steel $(0\mathrm{.}5wt\%C)($Fig$.2).$

Fig. $1Fe-F{e}_{3}C$ phase diagram diagram for a hypoeutectoid steel $(0\mathrm{.}5wt\%C).$

$($b$)(5$ points$)$ If a thin specimen of hypoeutectoid steel above is

quenched instantaneously from $900$ to $550C,$ held for $1$ second, and quenched to room temperature, what phases will be present in the microstructure.

$($c$)(5$ points$)$ Superimpose the continuous cooling transformation diagram for a hypoeutectoid steel $(0\mathrm{.}5$ wt$\%$ C$)$ in Fig. $2.$

$($d$)(5$ points$)$ When a thin specimen of hypoeutectoid steel above is cooled continuously from $900C$ to room temperature, what is the minimum cooling rate to obtain $100\%$ martensite. Explain the details of your calculation.