Question

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

Answer 1

Given: The diameter of the sphere $=18cm.$
So, Radius $=9cm.$
The volume of a sphere $=\frac{4\pi r^3}{3}=\frac{4\pi (9{)}^3}{3}=972\pi c{m}^3$

Since volume is constant even after melting

The volume of the long wire will also be equal to $972\pi c{m}^3$

The length of wire $=108m=10800cm.$

The long wire is assumed to be the cylinder.

So volume of the long cylindrical wire $=\pi r^{2}h$

$\therefore \pi r^2\times 10800=972\pi$

$\Rightarrow r^2=\frac{972}{10800}$

$\Rightarrow r^2=0.09$

$\Rightarrow r=\sqrt{0.09}=0.3cm$

Diameter of the long cylindrical wire, $d=2r=2\times 0.3=0.6cm$