Question

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.

Answer 1

Ans : Diameter : 0.06cm.

Diameter of the sphere is 18 cm.
Radius is 9cm.
The volume of a sphere is $\frac{4\pi (9{)}^3}{3}$ = $972\pi c{m}^3$.
Since volume is constant even after melting The volume of long wire is also $972\pi c{m}^3.$
Length of wire is 108 m=10800 cm.
The long wire is assumed to be cylinder.
So volume = $\pi r^{2}h$ = 972 $\pi$

But h = 10800 cm
$r^2$ = $\frac{972\pi }{10800\pi }$ = 0.09
r = √0.09 = 0.3 cm

d = 2r = 2$\times$ (0.3) = 0.6 cm