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Assume a uniform neutron density $n(x,y,z_0)=1\mathrm{.}0[$neutrons $\frac{?}{c{m}^3}]$ at the surface $z=z_0$ for neutrons traveling in direction hat$()=({}_x,{}_y,{}_z)=(\frac{\sqrt[\phantom{2}]{2}}{2},0,\frac{\sqrt[\phantom{2}]{2}}{2})$ with energy $E=0\mathrm{.}025eV[$illustrated in picture above$].$ Calculate the total rate at which $0\mathrm{.}025eV$ neutrons are passing through the $3cm4cm$ surface in direction hat$().$Assume neuton velocity is $2\mathrm{.}2$x$105$ cm$/$sec