# Computing Poisson ratio

question

A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa

my attempt

D original = 0.01m
change in D = 0.000007m
F=15000N
E= 100*10^9

V = passonse ratio = (change in D/D original)/(change in L/ L original)

we can replace (change in L/ L original) by (stress/E)

so

V=(change in D/D original)/(stress/E)

(change in D/D original) = (0.000007/0.01)
(stress/E) = (F/Area)/E
A= pi(0.01/2)^2

that gives me an answer of V = 0.21

but the tutorial sheet says the answer is 0.33

can you explain where i have gone wrong

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