$1.$ A $\backslash (0\mathrm{.}40\backslash \%\backslash$mathrm$\{$C$\}\backslash )$ steel is slowly cooled down from $\backslash (940^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to a temperature just slightly above $\backslash (727^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

a$)$ Calculate the weight percent austenite present in the steel.

b$)$ Calculate the weight percent proeutectoid ferrite present in the steel.

c$)$ What is the composition in each phase

$2.$ Further cool the steel down to slightly below $\backslash (727^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

a$)$ Calculate the weight percent ferrite and cementite present in the steel.

b$)$ Composition in each phase

c$)$ Calculate the weight percent eutectoid ferrite and weight percent eutectoid cementite present in the steel.