Question

1. If the diameter of the cross-section of a wire is decreased by 5%, by what percentage
should the length be increased so that the volume remains the same?
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Answer 1

Answer:

diametre be d

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%

hope it helps