The length of the wire is approximately 3600 cm.
How to calculate length?
Volume of a sphere = (4/3)πr³
Radius (r) of the sphere is half the diameter, so
r = 6 cm / 2
= 3 cm
Volume of the sphere = (4/3)π × 3 cm³
≈ 36π cm³
Volume of a cylinder = πr²h,
where h = height (thickness) of the cross-section.
Radius (r) of the wire's cross-section is half the diameter, so
r = 0.2 cm / 2
= 0.1 cm
Since the volume of the sphere is equal to the volume of the wire (assuming no material is lost during melting and drawing), equate the two volume equations:
36π cm³ = π × 0.1² cm² × h
Solving for h:
h = 36π cm³ / (π × 0.01 cm²)
≈ 3600 cm
Therefore, the length of the wire is approximately 3600 cm.