$(6)$ A hypothetical face$-$centred cubic metal has a lattice parameter $\backslash ($ a$=0\mathrm{.}400\backslash$mathrm$\{$~nm$\}\backslash ).$ A single crystalline bar made from the metal has a length of $20$ mm and a diameter of $2$ mm $.$ The Burgers vector of dislocations in the metal is Assuming only one slip system is activated during uniform tensile straining and the angle between the direction of the Burgers vector of the dislocations and the tensile direction is $\backslash (60^\{\backslash$circ$\}\backslash ).$ Calculate the number of dislocations needed to achieve an engineering plastic strain of $\backslash (10\backslash \%\backslash ).(15\backslash \%)$