Question

The diameter of a copper sphere is 18 cm. It is 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

Diameter : 0.06cm. procedure:
Diameter of sphere is 18 cm.
Radius is 9cm.
Volume of sphere is $\frac{4\times \pi \times 9^3}{3}=972\pi c{m}^2$
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 = $\pi \times r^2\times h=972\pi$
But $h=10800cm\times r\times r=\frac{972\pi }{10800\pi }=0.09\times r=\sqrt{0}.09=0.03cm\times d=2\times r=2\left(0.03\right)=0.06cm$