document.write( "Question 1006486: a wire cross section diameter decresed 5% then volumes equal which percentage length increased
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Algebra.Com's Answer #622775 by KMST(5328) $\"\"$ $\"About$

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If the diameter decreases by $\"%225%25%22\"$ ,
\n" ); document.write( "it becomes $\"%22100%25%22-%225%25%22=%2295%25%22=95%2F100=0.95\"$ of the original diameter.
\n" ); document.write( "As a consequence, the cross-section surface area,
\n" ); document.write( " $\"area=pi%2Adiameter%5E2%2F4\"$ ,
\n" ); document.write( "becomes
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.
\n" ); document.write( "It becomes $\"0.9025=90.25%2F100=%2290.25%25%22\"$ of the original cross-section surface area.
\n" ); document.write( "As the wire can be considered a cylinder,
\n" ); document.write( "with a base the same size/shape as the circular cross-section,
\n" ); document.write( "and the length of the wire for a height,
\n" ); document.write( "the original wire's volume is
\n" ); document.write( " $\"volume=area%2Alength\"$ .
\n" ); document.write( "The new wire's volume is
\n" ); document.write( " $\"new_volume=new_area%2Anew_length=0.9025%2Aarea%2Anew_length\"$ .
\n" ); document.write( "Since that volume has to be the same,
\n" ); document.write( " $\"0.9025%2Aarea%2Anew_length=area%2Alength\"$ --> $\"0.9025%2Anew_length=length\"$ --> $\"new_length=length%2F0.9025\"$
\n" ); document.write( "The relative change in length is
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$\"%28rounded%29=10.8033%2F100\"$ $\"%28rounded%29=%2210.8033%25%22\"$ $\"%28rounded%29\"$ .
\n" ); document.write( "We cannot give an exact decimal value,
\n" ); document.write( "we have to give a rounded, approximate result,
\n" ); document.write( "as $\"%2210.8%25%22\"$ , or $\"%2211%25%22\"$ , for example,
\n" ); document.write( "because $\"1%2F0.9025\"$ and $\"1%2F0.9025-1\"$ written as decimals would have an infinite number of digits.
\n" ); document.write( "Since we start with two significant figure in $\"%2295%25%22\"$ ,
\n" ); document.write( "reporting the result as $\"%2210.8%25%22\"$ (very similar precision),
\n" ); document.write( "or $\"%2211%25%22\"$ (same number of significant digits) makes sense.
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\n" ); document.write( "NOTE:
\n" ); document.write( "If all that talk about precision and significant figures, doesn't make sense to you, pretend that I did not write that. \n" ); document.write( "

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