Answer
$N_A=6.0223\times10^{23}$
Work Step by Step
Volume: $(286.65\times10^{−10} cm)^3=2.355\times10^{−23} cm^3$
Mass: $7.874\ g/cm^3×2.355\times10^{−23} cm^3=1.855\times10^{−22} g$
$1.855\times10^{−22}\ g=(2×55.845)\ g/mol\div N_A$
$N_A=6.0223\times10^{23}$