document.write( "Question 1114772: A metal cube expands due to it being heated. When the length of an edge of the cube is 4 cm, the volume of a metal cube is increasing at the rate of 0.63 cm3 s-1. What is the rate of change of an edge at this time? \n" ); document.write( "
Algebra.Com's Answer #729742 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "The volume of the cube is given by the equation
\n" ); document.write( "\"V+=+s%5E3\"

\n" ); document.write( "The relationship between the rate of change of volume and the rate of change of edge length is found by differentiating that equation:
\n" ); document.write( "\"dV%2Fdt+=+3s%5E2%2A%28ds%2Fdt%29\"

\n" ); document.write( "It is given that the volume is increasing at a rate of 0.63 cm^3/sec when the edge length is 4 cm, so

\n" ); document.write( "\"0.63+=+3%284%5E2%29%2A%28ds%2Fdt%29\"
\n" ); document.write( "\"ds%2Fdt+=+0.63%2F48+=+0.013125\"

\n" ); document.write( "Answer: At the moment when the edge length is 4 cm, it is increasing at the rate of 0.013125 cm/sec.
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