Question

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

Answer 1

Side of a solid cube $=7.2cm$

$\therefore$ Volume $=(Side{)}^3=(2.2{)}^3$

$=10.648c{m}^3$

$\therefore$ Volume of cylindrical wire $=10.648c{m}^3$

Radius $=1mm$ $=\frac{1}{10}cm$

$\therefore$ Length $=\frac{Volume}{\pi r^2}$

$=\frac{10.648\times 7\times 10\times 10}{22\times 1\times 1}$

$=\frac{10648\times 7\times 100}{1000\times 22}=\frac{484\times 7}{10}cm$

$=\frac{3388}{10}=338.8cm$
Hence, the length of the wire $=338.8cm$