document.write( "Question 718514: The volume V of a cylindrical can is v=(pi)r^2h, where r is the radius of the base, and h is the heighth of the cylinder. if the radius of the cylinder is decreased by 25%, by how many % should its heighth icrease, so that the cylinder has the same volume v? round your answer to the nearest 10th of a %. \n" ); document.write( "

Algebra.Com's Answer #440932 by josgarithmetic(39617) $\"\"$ $\"About$

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Let's call the initial height, h and the increased height, H. We want initial and increased volumes to be the same.
\n" ); document.write( "I am using normal fraction form in the steps. 25% decrease means 1/4 decrease, meaning 3/4 of original value for r. \r
\n" ); document.write( "\n" ); document.write( "V= $\"pi%2Ar%5E2%2Ah=pi%28%283%2F4%29r%29%5E2%2AH\"$
\n" ); document.write( " $\"pi%2Ar%5E2%2Ah=pi%2Ar%5E2%283%2F4%29%5E2%2AH\"$
\n" ); document.write( " $\"h=%283%2F4%29%5E2%2AH\"$ , divided by sides by $\"pi%2Ar%5E2\"$
\n" ); document.write( " $\"h%2F%28%283%2F4%29%5E2%29=H\"$ , divided both sides by $\"%283%2F4%29%5E2\"$
\n" ); document.write( " $\"1%2F%28%283%2F4%29%5E2%29=H%2Fh\"$ , divided both sides by h. \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28H%2Fh=16%2F9%29\"$ , we want this ratio because this is how many times h must be increased to become H, to keep V the same. You can convert into its percent increase if desired. \n" ); document.write( "

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