Given,

Diameter of the copper Rod = 2cm

Length of the Rod = 10 cm

Length of the wire = 10 m = 1000cm

So here we have,

Radius of the copper rod = 1 cm

Let suppose the radius of the wire = r

Volume of the rod = volume of the wire

πr²h = πr²h

1 × 1 × 10 = 1000 × r

10 = 1000r

r = = 0.1 cm

The diameter of the wire = 2r = 2 × 0.1 = 0.2 cm

So, the thickness of the wire is 0.2 cm or 2mm.