The length of the wire is 36 m.
Explanation:
Given, Diameter of sphere = 6 cm
We know that, radius can be found by taking the half in the diameter value. So,
[tex]\text { sphere radius, } R=\frac{D}{2}=\frac{6}{2}=3 \mathrm{cm}=3 \times 10^{-2} \mathrm{m}[/tex]
Similarly,
[tex]\text { wire radius, } r=\frac{0.2}{2}=0.1 \mathrm{mm}=1 \times 10^{-3} \mathrm{m}[/tex]
We know the below formulas,
[tex]\text {volume of sphere}=\frac{4}{3} \times \pi \times R^{3}[/tex]
[tex]\text {volume of wire}=\pi \times r^{2} \times l[/tex]
When equating both the equations, we can find length of wire as below, where [tex]\pi=\frac{22}{7}[/tex]
[tex]\frac{4}{3} \times \pi \times R^{3}=\pi \times r^{2} \times l[/tex]
[tex]\frac{4}{3} \times \frac{22}{7} \times\left(3 \times 10^{-2}\right)^{3}=\frac{22}{7} \times\left(1 \times 10^{-3}\right)^{2} \times l[/tex]
The [tex]\pi[/tex] value gets cancelled as common on both sides, we get
[tex]\frac{4}{3} \times 27 \times 10^{-6}=10^{-6} \times l[/tex]
The [tex]10^{-6}[/tex] value gets cancelled as common on both sides, we get
[tex]l=4 \times 9=36 m[/tex]
