In the electric currect flow, it is found that the resistance (measured in the units called ohms) offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. if a wire 0.01 in. in diameter has a resistance of 0.331 0.331 ohm, what is the resistance of a wire of the same length and material with diameter 0.0182 0.0182 in. to the nearest ten-thousandth?

so... when something varies inversely in relation to something else, usually means y = k/x  or thereabouts, with "k" the constant of variation, being a constant divided by the denominator

so, in this case  the resistance say "r", varies inversely to the square of the diameter "d", that simply means 
so, what the dickens is "k" then?

now, we know that, the resistance is 0.01 when the diameter is 0.331

that simply means   

now... what is the resistance "r" when d=0.0182?   well, 

Ithink the answer is d.