The diameter of a copper sphere is 18 cm, It melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

Ans : Diameter : 0.06cm.

Diameter of the sphere is 18 cm.
Radius is 9cm.
The volume of a sphere is $\frac{4\pi (9{)}^3}{3}$ = 972π square cm.
Since volume is constant even after melting The volume of long wire is also 972π square cm Length of wire is 108 m=10800 cm.
The long wire is assumed to be cylinder. So volume = $\pi$ $\times$ r $\times$ r $\times$ h = 972 $\pi$

But h = 10800 cm r $\times$ r $\times$ = $\frac{972\pi }{10800\pi }$ = 0.09
r = √0.09 = 0.03 cm

d = 2r = 2$\times$ (0.03) = 0.06 cm