Question

Find the length of 13.2 kg of copper wire of diameter 4mm when 1 cube cm of copper weighs 8.4 gm.

Answer 1

Weight of wire = 13.2 kg
Diameter of wire = 4mm
$\therefore$ Radius(r) = $\frac{4}{2}=2mm=0.2mm$
Let he be the length of wire
$\therefore$ Volume = $\pi r^{2}h=\frac{22}{7}\times (0.2{)}^{2}hc{m}^3$
Weight of 1 cu.cm copper= 8.4 gm
$\therefore$ Total weight
$\frac{22}{7}\left(0.04\right)h\times 8.4gm$
According to the condition,
$\frac{22}{7}\times 0.04\times h\times 8.4=13.2\times 1000$
$h=\frac{13.2\times 1000\times 7}{22\times 0.04\times 8.4}$
$=\frac{132\times 1000\times 7\times 100\times 10}{10\times 22\times 4\times 84}=\frac{100000}{8}cm$
$=12500cm=\frac{12500}{100}=125m$