Resistivity of a stretched wire VS unstretched state

[SpecialMen]

1. A wire of a 6.0$$\Omega$$ resistance is stretched to three times its original length. Assume the diameter and resistivity have stayed the same, what is its new resistance?



2. R=$$\stackrel{\rho L}{A}$$



3. Since the only thing that's changed in the equation is L, having tripled, I was obviously thinking the resistance would now be 18$$\Omega$$, but the books answer is 54$$\Omega$$. What am I doing wrong?

 

[Mapes]

Hi SpecialMen, welcome to PF. When metals are plastically deformed, it's usually assumed that the volume remains constant, not the cross-sectional area. Know what I mean?

 

[SpecialMen]

Hi SpecialMen, welcome to PF. When metals are plastically deformed, it's usually assumed that the volume remains constant, not the cross-sectional area. Know what I mean?

Thanks, I appreciate the welcoming!
And yes, I know exactly what you mean. This is what I told myself when I first read the question, thinking it was strange to neglect the change in diameter of the cable...I reread the question a couple times, and then realized that what the book really said was we were assuming the same resistivity and density, not diameter as I had originally read. Brain freeze, I've been doing these problems for the past 6 hours, literally! Still, thanks for yor input! Would have gotten me out of my hole had I not reread the question!