Question

A 14.0 ohm resistor is made from a coil of copper wire whose total mass is 23.0 g. What is the diameter of the wire, and how long is it?

Answer 1

need conductivity of copper, in your book, call it c
need density of copper, call it rho

1/R = 1/14 = c(pi r^2)/L
but
rho pi r^2 L = 23 grams= .023 kg

so
pi r^2 = .023/(rho L)
so
1/14 = c (.023/(rho L^2))
solve for L etc
make sure you use consistent units. I am assuming meters, kilograms, seconds