Question

A piece of gold wire has a diameter of 0.175 cm. How much will precisely 1.00 x 10^5 of the wire weight?

Answer 1

Given data:

Diameter of the gold wire (d) = 0.175 cm

Length of the gold wire (l) = 1.00 * $10^{5}$ cm

Volume of the given gold wire = volume occupied by a cylindrical object\

                                       = π * $r^{2}$*l

here r = radius of the cross section

where : r = d/2

Hence the volume V = π * $(d/2)^{2}$*l

            = $3.142 * (0.175/2)^{2} * 1.00*10^{5} = 2.41 * 10^{3} cm^{3}$

Density of gold = 19.3 g/cm3

Weight of the gold wire = Density * volume

= $19.3 g/cm^{3}$ * $2.41*10^{3} cm^{3}$

= $4.65 * 10^{3} g = 4.65 kg$