SOLUTION: a wire cross section diameter decresed 5% then volumes equal which percentage length increased

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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