A $1$ cm bimetallic copper$-$silver wire diameter, prepared by co$-$extrusion with copper as core and silver as layer exterior. The desired properties along

of the axis parallel to the length of the bimetallic wire are:

a$)$ Thermal conductivity $>410$ W$/($m K$)$;

b$)$ Electrical conductivity $>603106\backslash$Omega $21$m$21,$ and

c$)$ Weight $<mtext></mtext><mn>7</mn><mn>5</mn><mn>0</mn>$ g$/$m$.$ Determine the permitted range of the diameter of the copper core.