Answer
$514\ m$
Work Step by Step
Calculate the mass of the spool in grams:
$m = 10\ lb\cdot \frac{453.92\ g}{1\ lb}=4539.2\ g$
Calculate the volume of the spool:
$d = \frac mV$
$V = 4593.2\ g\div 2.70 g/cm^3=1701.2\ cm^3$
Calculate the radius of the wire in cm:
$r = \frac d2$
$r = (0.0808\ in\div 2)\cdot \frac{2.54\ cm}{1\ in}=0.103\ cm$
Calculate the length of the spool in meters:
$V=\pi r^2\ell$
$\ell=1701.2\ cm^3\div(\pi\cdot (0.103\ cm)^2)\cdot\frac{1\ m}{100\ cm}$
$\ell=514\ m$
