Assume that $1\mathrm{.}0kg$ of cartridge brass $($an FCC solid solution alloy comprised of $70$ wt$.\%$ Cu$-30$ wt$.\%$ Zn$)$ has been cold worked to achieve a dislocation density $($perfect basis$)$ of $1\mathrm{.}0({10}^{12})c{m}^{-2}.$ Further assume that all these dislocations are separated into pairs of partial dislocations with stacking faults lying between the partials $($i$.$e$.,$ the partial dislocation density is $2\mathrm{.}0({10}^{12})c{m}^{-2}).$ Use Fig. $18\mathrm{.}17$ to assist you in estimating the total area $($in $c{m}^2)$ of such stacking faults in $1\mathrm{.}0kg$ of cartridge brass.

$($hint: $(1).$ The rule of mixtures applies to the lattice parameter in brass; $(2)$ The shear modulus of cartridge brass is the same as the shear modulus of pure $Cu$; $(3)$ The density of dislocation is measured by length per unit volume, e$.$g$.,c\frac{m}{c}{m}^3,$ which gives $c{m}^{-2})$

$30wt.\%Zn,$ the stacking fault energy is $14m\frac{J}{m^2})$