document.write( "Question 1065354: A pool with a volume of 1000 gallons requires a cover that is 250 sq. ft. What size cover is appropriate for a similarly-shaped pool that holds 3375 gallons? \n" ); document.write( "

Algebra.Com's Answer #680505 by KMST(5328) $\"\"$ $\"About$

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When you \"scale up\" (or down) a shape,
\n" ); document.write( "to a similar shape where all dimension measurements
\n" ); document.write( "are changes by a factor $\"k\"$ ,
\n" ); document.write( "the length ratio is $\"k\"$ for all lengths,
\n" ); document.write( "the surface area ratio is $\"k%5E2\"$ for al surfaces,
\n" ); document.write( "and the volume ratio is $\"k%5E3\"$ for the one and only volume.
\n" ); document.write( "In this case,
\n" ); document.write( " $\"k%5E3=3375%2F1000=15%5E3%2F10%5E3=%2815%2F10%29%5E3\"$ ,
\n" ); document.write( "so $\"k=15%2F10\"$ and $\"k%5E2=%2815%2F10%29%5E2=15%5E2%2F10%5E2=225%2F100\"$ .
\n" ); document.write( "Applying that factor to 250 square feet,
\n" ); document.write( "we find the size (in square feet) of the larger pool to be
\n" ); document.write( " $\"250%2A%28225%2F100%29=250%2A226%2F100=562.5\"$ \n" ); document.write( "

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