Chapter 3 - Polynomial and Rational Functions - 3.6 Variation - 3.6 Exercises - Page 389: 37

$0.0444\ ohm$

Step 1. Assume $R\ (ohm)$ is the the resistance offered by a fixed length of wire of a given material. Step 2. Assume $d\ (in)$ is the diameter of the wire. Step 3. From the given conditions, we have $R=k/d^2$ and $0.4=k/(0.01)^2$, thus $k=4\times10^{-5}$ Step 4. For $d=0.03\ (in)$, we have $R=4\times10^{-5}/(0.03)^2\approx0.0444\ ohm$