Question

If the diameter of cross section of wire is decreased by 5%. How much percent will the length be increased so that the volume remains the same

Answer 1

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%

Thank you and best of luck :)