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The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, find the radius of its cross-section.
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The wire is in the shape of a cylinder.
Since the sphere is melted and a cylindrical wire is formed, their volumes are equal.
Volume of a sphere =
3
4
πr
3
As the diameter of the sphere is 6 cm, its radius r=3 cm
Volume of a Cylinder =πR
2
h
Length of the wire h=36m=3600cm
Hence, Volume of sphere = Volume of the wire
3
4
πr
3
=πR
2
h
R
2
=
100
1
R=
10
1
=0.1cm
Hence, radius of the cross-section of the wire =0.1cm
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