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

V = pi.h.r^2 (cylinder)

When diameter is decreased by 5%, radius also is decreased by 5%. So new radius is 19r/20.

So V becomes pi.h.(19r/20)^2 = pi.h.(361r^2)/400.

But you want to maintain the volume at a constant, so h is to be multiplied by 400/361 to keep it constant.

So length is to be incresed by 400/361 - 1 = 39/361 times, i.e. 39 x 100/361 = 10.8033 %

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