$($a$)$ Sketch and label the microstructural changes that occur in hyper$-$eutectoid steel during equilibrium cooling from $900C$ to room temperature.

$($b$)$ For an $Fe-0\mathrm{.}35C$ alloy at a temperature just below the eutectoid, determine $($i$)$ fraction of ferrite and cementite phases, $($ii$)$ fraction of ferrite and pearlite and $($iii$)$ fraction of eutectoid ferrite.