Answer :
Answer : The length of the wire is, 8533 cm
Step-by-step explanation :
As the iron sphere is beaten and drawn into a wire. That means, their volume will be equal.
Volume of iron sphere = Volume of cylindrical wire
The formula will be:
[tex]\frac{4}{3}\pi r_1^3=\pi r_2^2h[/tex]
where,
[tex]r_1[/tex] = radius of sphere = [tex]\frac{Diamtere}{2}=\frac{8cm}{2}=4cm[/tex]
[tex]r_2[/tex] = radius of cylindrical wire = [tex]\frac{Diamtere}{2}=\frac{2mm}{2}=1mm=0.1cm[/tex]
h = height of cylindrical wire or length of wire
Now put all the given values in the above formula, we get:
[tex]\frac{4}{3}\pi r_1^3=\pi r_2^2h[/tex]
[tex]\frac{4}{3}\times r_1^3=r_2^2h[/tex]
[tex]\frac{4}{3}\times (4)^3=(0.1)^2h[/tex]
[tex]h=8533.33cm\approx 8533cm[/tex]
Therefore, the length of the wire is, 8533 cm