Why does the thinner wire experience 4 times the stress, not 8 times?

[BrainMan]

Homework Statement

Two wires are made of the same metal but have different dimensions. Wire 1 is 4 times longer and twice the diameter of wire 2. If they are both under the same load, compare (a) the stresses in the two wires and (b) the elongations of the two wires.

Homework Equations

stress = F/A
elongation = ΔL/L

The Attempt at a Solution

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For the first part I did
F/A
F/((x/2)^2*3.14)
2F/3.14x^2

F/A
F/((x/4)^2*3.14)
16F/3.14x^2

So it should be that the thinner wire experiences 8 times as much stress as the thicker wire. However the correct answer is that the thinner wire experiences 4 times as much stress.

 

[PhanthomJay]

You forgot to square the 2 in your first equation .
Elongation is change in length. You have written the equation for strain.

 

[BrainMan]

You forgot to square the 2 in your first equation .
Elongation is change in length. You have written the equation for strain.

Ok I figured it out. Thanks!