document.write( "Question 1186790: All edges of a cube are expanding at a rate of 5 centimeters per second.\r
\n" ); document.write( "\n" ); document.write( "(a) How fast is the surface area changing when each edge is 3 centimeters?\r
\n" ); document.write( "\n" ); document.write( "(b) How fast is the surface area changing when each edge is 10 centimeters?
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Algebra.Com's Answer #817761 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "These are related-rates problems.\r
\n" ); document.write( "\n" ); document.write( "(a)
\n" ); document.write( "The surface area of a cube of side a is:
\n" ); document.write( "S = \"+6%2Aa%5E2+\" \r
\n" ); document.write( "\n" ); document.write( "The rate of change of surface area, with respect to t, is:
\n" ); document.write( "\"dS%2Fdt\" = \"dS%2Fda\"\"da%2Fdt\"\r
\n" ); document.write( "\n" ); document.write( "\"dS%2Fda\" = 12a \"cm\"
\n" ); document.write( "\"da%2Fdt\" = 5cm/s (given)\r
\n" ); document.write( "\n" ); document.write( "So we can write:
\n" ); document.write( "\"dS%2Fdt\" = \"12a+%2A+5+\" = \"60a\" \"cm%5E2%2Fs\" (*)\r
\n" ); document.write( "\n" ); document.write( "So at a=3cm, the surface area is changing at
\n" ); document.write( "\"dS%2Fdt\" = 12(3)cm * 5cm/s = 180\"cm%5E2%2Fs\" \r
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\n" ); document.write( "\n" ); document.write( "(b) plug a=10cm into (*) \n" ); document.write( "
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