Question

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

Answer 1

For sphere: $d=18cm$ therefore, $r=9cm$

For cylinder: $h=10800cm$ and $R=?$

As the sphere is melted down into cylindrical wire, therefore,

The volume of sphere $=$ Volume of wire

$\frac{4}{3}\pi r^3=\pi R^{2}h$

$\Rightarrow \frac{4}{3}\times 9\times 9\times 9=R^2\times 108\times 100$

$\Rightarrow R^2=\frac{4\times 9\times 9\times 9}{3\times 108\times 100}=0.09$

$\Rightarrow R=0.3$

So, $\text{diameter}=2R=0.6cm$.