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**1. A wire with a resistance of 6ohms is drawn out through a die so that its new length is three times its original length. Find the resistance of the longer wire, assuming that the resistivity and density of the material are unchanged.**

**R = p (L/A)**

Working out this problem I came across two different methods. When I initially looked at the problem my first reaction was to use integration which lead me to do this

R`= 6

(6/3) =

**2**. then R =(6^2) *(3/

**2**) =54

the other method led me to do this 3/(1/3) = 9 then 9*6 = 54

Are they both not correct ways of doing it? My friend says I just pulled Numbers out of my hat and got lucky. But I can get the same answer both ways on any problem. Would the first way not be a correct way of integrating?