Question

The diameter of a metallic sphere is $6cm$. It is melted and drawn into a wire having diameter of the cross-section as $0.2cm$. Find the length of the wire.

Answer 1

We have
Diameter of metallic sphere $=6cm$
Radius of metallic sphere $=3cm$
Also we have
Diameter of cross-section of cylindrical wire$=0.2cm$
$\therefore$ Radius of cross-section fo cylindrical wire$=0.1cm$
Let the length of the wire be $h$ cm
Since the metallic sphere is converted into a cylindrical shaped wire of length $h$ cm
Volume of the metal used in wire$=$ Volume of the sphere

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

$\Rightarrow \pi \times {\left(0.1\right)}^2\times h=\frac{4}{3}\times \pi \times 3^3$
$\Rightarrow \pi \times {\left(\frac{1}{10}\right)}^2\times h=\frac{4}{3}\times \pi \times 27\Rightarrow \pi \times \frac{1}{100}\times h=36\pi$

$\Rightarrow h=\frac{36\pi \times 100}{\pi }cm=3600cm=36metres$

$\therefore$ Length of the wire$=3600cm$