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`