# IF the diameter of the cross section of a wire is decreased by 5% how much% will the length be increased so that its volume remains same

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radius be d/2

vol=πr*r*h

=πd*d*h/4

if d is increased by 5% then d- 5%of d

d-5/100*d

d-d/20

19d/20

∴r=2*19d/20=19d/40

vol=πd*d*h/4

π*19d/40*19d/40*h

∴h=400d/361 ( calculate the above one)

increase in length=400h/361-l

=39l/361

%of increase =39h/361/h*100=3900/361% =10.80%