Problem $4-$ Fire analysis of light framed assemblies

A wood$-$stud framed wall assembly is made of $2"$ x $4"(38mm89mm$ studs at $16"(406$

$mm)$ on centre. The assembly is protected with one layer of $\frac{5}{8}"(15\mathrm{.}9mm)$ Type X gypsum

board on one side and another layer of $\frac{1}{2}"(12\mathrm{.}7mm)$ Type X gypsum board on the second

side. Determine the fire resistance rating, under standard fire exposure, of the wall assembly:

$($a$)$ If the cavity is filled with glass fiber insulation

$($b$)$ If the cavity is filled with rock wool insulation

$($c$)$ If the cavity is left unfilled.