Question

A soild cube of metal each of whose sides measures 2.2 cm is melted to form a cylindrical wire of radius 1 mm. Find the length of the wire so obtained.

Answer 1

First, Volume of Cube = Volume of wire
so V(Cube) = $s^3$
$s=2.2=\frac{22}{10}$
$V={\left(\frac{22}{10}\right)}^3$
$=22\times 22\times \frac{22}{1000}$
Volume of wire also be = $22\times 22\times \frac{22}{1000}$
volume of cylinder $\pi r^{2}h$
Radius = 1mm; h = ?
As, 1cm = 10mm; so, $1mm=\frac{1}{10}cm$
$22\times 22\times \frac{22}{1000}=\frac{22}{7}\times {\left(\frac{1}{10}\right)}^2\times h$
$h=\frac{22\times 22\times 22\times 100\times 7}{1000\times 22\times 1}$
$=3288÷10$
=32.88 cm