Question

$2.2cubicdm$ of brass is to be drawn into a cylindrical wire $0.25cm$ in diameter. Find the length of the wire.

Answer 1

Volume of brass $=2.2cu.dm$

$=2.2\times 10\times 10\times 10=2200c{m}^3$ [$\because 1dm=10cm$]

Diameter of wire $=0.25cm$

$\therefore$ Radius $\left(r\right)=\frac{0.25}{2}=0.125cm$

Let ${}^{\prime }{h}^{\prime }$ be the length of wire, then

Volume of the wire $=\pi r^{2}h$

$\therefore \pi r^{2}h=2200$ [$\because$ Volume of the wire $=$ Volume of the brass]

$\Rightarrow \frac{22}{7}\times (0.125{)}^2\times h=2200$

$\Rightarrow h=\frac{2200\times 7}{22\times 0.125\times 0.125}cm$

$\Rightarrow h=\frac{2200\times 7\times 1000\times 1000}{22\times 125\times 125}cm$

$\Rightarrow h=44800cm=\frac{44800}{100}m=448m$

$\therefore$ Length of wire $=448m$