$($a$)$ Figure $1$ exhibits a phase diagram of $Pb-$Sn alloy system. Using it solve following problems:

$($i$)$ What are the compositions and relative amounts of the phases that constitute the eutectic microstructure?

$($ii$)$ For an alloy containing $30\%Sn,$ what are the relative amounts of $$ and $$ phases present at the eutectic temperature?

$($iii$)$ Again for an alloy containing $30\%Sn,$ what are the relative amounts of the eutectic and the proeutectic $$ phase present at the eutectic temperature?

$($b$)$ Draw the microstructural changes of hypoeutectoid, eutectoid and hypereutectoid steels at different temperatures during slow cooling from austenitic temperature to room temperature.