The length of the wire is 36 m.
The density is the ratio of the mass and volume of a substance. The density is given by the formula,
d=m/V
where d is the density. m is the mass and V is the volume.
The density of the material does not change and the initial and final volume of the substance will be equal when it has changed shape provided the mass has not been changed.
The radius r of the sphere is half of its diameter. Therefore, r=6.0/2 = 3.0 cm.
Then volume of the sphere Vs is given by the formula,
Vs=(4/3)*π*r^3
Put the value of r in the above formula.
Vs=(4/3)*3.14*(3.0)^3
Vs=113.04 cm^3
For the cylinder, the radius s=0.2/2 mm = 0.01 cm and the length l is unknown. The volume of the cylinder Vc is given by the formula,
Vc=πs^2l
Put s=0.01 cm in this equation and solve it.
Vc=(3.14)*(0.01)^2l
Vc=0.000314 l cm^2
The volume of the wire (cylindrical in shape) and the sphere are same, therefore,
Vc=Vs
0.000314 l =113.04
l=3600 cm
I=36 m.
Hence the length of the wire is 36 m.
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