A hypothetical face$-$centered cubic metal has a lattice parameter a $=0\mathrm{.}400$ nm$.$ 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 $<110>/2.$ 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 $60.$ Calculate the number of dislocations needed to achieve an engineering plastic strain of $10\%.(15\%)$