Explanation:

Given,
Diameter of the metallic sphere = 9 cm
Radius of the metallic sphere = 9/2 cm =4.5 cm
Volume of the sphere = 4/3∏×r³
= 4/3∏×4.5³
= 381.703 cm³ …………………………………….. (i)
Diameter of the cylindrical wire = 2 mm = 2/10 cm = 0.2 cm
The radius of the cylindrical wire be = 0.2/2 cm = 0.1 cm
Let the height of the cylindrical wire be = h cm
Volume of the cylindrical wire = ∏×r²×h
= ∏×0.1²×h…………….(ii)
Since the metallic sphere is melted and recast into a long cylindrical wire.
So comparing and equating both the above-marked equations
We get,
381.703 = ∏×0.1²×h…………….(ii)
H= 12150 =12150 cm
The required length of the wire after recasting of the metallic sphere is 12150 cm.