Question 1006486: a wire cross section diameter decresed 5% then volumes equal which percentage length increased
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If the diameter decreases by  ,
it becomes  of the original diameter.
As a consequence, the cross-section surface area,
 ,
becomes
 .
It becomes  of the original cross-section surface area.
As the wire can be considered a cylinder,
with a base the same size/shape as the circular cross-section,
and the length of the wire for a height,
the original wire's volume is
 .
The new wire's volume is
 .
Since that volume has to be the same,
 --> -->
The relative change in length is
    .
We cannot give an exact decimal value,
we have to give a rounded, approximate result,
as  , or  , for example,
because  and  written as decimals would have an infinite number of digits.
Since we start with two significant figure in  ,
reporting the result as (very similar precision),
or (same number of significant digits) makes sense.
NOTE:
If all that talk about precision and significant figures, doesn't make sense to you, pretend that I did not write that.
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