Solution:

Given diameter of the metallic sphere = 6 cm

Radius of the sphere, r = 6/2 = 3 cm

Volume of the sphere, V = (4/3)r³

= (4/3)××3³

= 4××9

= 36 cm³

Length of the wire, h = 36 m = 3600 cm

Since the sphere is melted and drawn into a wire, volume remains the same.

Volume of the wire, r²h = 36

r²×3600 = 36

r² = 1/100

r = 1/10 = 0.1 cm = 1 mm

Hence the radius of the wire is 1 mm.