Lead needed to coat a cable

Submitted by MichMaganda on

How much lead is needed to coat a cable, 55mm in diameter, if the cable is 5km long and the lead coat is 4mm thick. 11.4x10^3 kg/m^3 for the density of the lead.

Jhun Vert Sun, 05/10/2015 - 08:12

Radius of uncoated cable = 55/2 = 27.5 mm = 0.0275 m
Radius of coated cable = 55/2 + 4 = 31.5 mm = 0.0315 m
Length of cable = 5000 m
 

Required volume of lead
$V = \pi (0.0315^2 - 0.0275^2)(5000) = 1.18\pi ~ \text{ m}^3$
 

Required mass of lead
$m = \rho V = (11.4 \times 10^3)(1.18\pi) = 42,260.70 ~ \text{ kg}$