$3.(8$ pts$)$ Using the isothermal transformation diagram $($TTT diagram$)$ for a $\backslash (0\mathrm{.}45\backslash$mathrm$\{$wt$\}\backslash \%\backslash$mathrm$\{$C$\}\backslash )$ steel alloy, answer the following questions. In each case, assume that the specimen begins at $\backslash (845^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenite structure. $($A: austenite, F: ferrite, P: pearlite, B: bair

$($a$)(4$ pts$)$ Determine the final microstructure $($in terms of the percentages of the microconstituents present$)$ when the specimen is rapidly cooled to $\backslash (400^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ held for $500$ sec $,$ then quenched to room temperature.

$($b$)(4$ pts$)$ Determine the final microstructure $($in terms of the percentages of the microconstituents present$)$ when the specimen is rapidly cooled to $\backslash (700^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ held at this temperature for $\backslash (10^\{6\}\backslash$mathrm$\{$sec$\}\backslash ),$ then quenched to room temperature.

PLEASE SOLVE AND EXPLAIN FULLY