document.write( "Question 747143: the percentage change in the surface area of a cube when each side is tripled is \n" ); document.write( "
Algebra.Com's Answer #454729 by KMST(5328)\"\" \"About 
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\"highlight%28800%29\"% \r
\n" ); document.write( "\n" ); document.write( "If the length of an edge of the cube is \"s\",
\n" ); document.write( "the surface area of each of the 6 faces of the cube is \"s%5E2\",
\n" ); document.write( "and the total surface area of the cube is \"6s%5E2\".
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\n" ); document.write( "If the length of the edge is tripled to \"3s\",
\n" ); document.write( "the surface area of each of the 6 faces of the cube is \"%283s%29%5E2=3%5E2s%5E2=9s%5E2\",
\n" ); document.write( "and the total surface area of the cube is \"6%289s%5E2%29=54s%5E2\".
\n" ); document.write( "The absolute change is \"54s%5E2-6s%5E2=48s%5E2\".
\n" ); document.write( "As a percentage of \"6s%5E2\", that is \"%2848s%5E2%2F6s%5E2%29%2A100=8%2A100=800\"%
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\n" ); document.write( "A factor of \"3\" change to a length, translates into a factor of \"3%5E2=9\" change to surface area, and it would translate into a factor of \"3%5E3\" change to the volume.
\n" ); document.write( "The generalization is true for any scale-up (or scale down) of any solid, by any factor.
\n" ); document.write( "If you reproduce the shape changing every length by a factor \"k\", the surface area changes by a factor \"k%5E2\" and the volume changes by a factor \"k%5E3\".
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