document.write( "Question 1040831: A gardening company is designing a rectangular compost container that will be twice as tall as it is wide and must hold 18 ft3 of composted food scraps. Find the dimensions of the compost container that has minimal surface area. (include the top and bottom of the container) \n" ); document.write( "

Algebra.Com's Answer #655749 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+W+\"$ = the width
\n" ); document.write( " $\"+2W+\"$ = the height
\n" ); document.write( "Let $\"+L+\"$ = the length
\n" ); document.write( "--------------------
\n" ); document.write( "given:
\n" ); document.write( " $\"+W%2A2W%2AL+=+18+\"$ ft3
\n" ); document.write( " $\"+2L%2AW%5E2+=+18+\"$
\n" ); document.write( " $\"+L%2AW%5E2+=+9+\"$
\n" ); document.write( " $\"+L+=+9+%2F+%28W%5E2%29+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Let $\"+S+\"$ = the inside surface area
\n" ); document.write( " $\"+S+=+2%2AW%2A2W+%2B+2%2AL%2A2W+\"$
\n" ); document.write( " $\"+S+=+4W%5E2+%2B+L%2A4W+\"$
\n" ); document.write( " $\"+S+=+4W%5E2+%2B+%28+9%2F%28W%5E2%29%29%2A4W+\"$
\n" ); document.write( " $\"+S+=+4W%5E2+%2B+36%2FW+\"$
\n" ); document.write( "Is this in a calculus course? If so take the
\n" ); document.write( "derivative of $\"+S+\"$ with respect to $\"+W+\"$
\n" ); document.write( "------------------------------------
\n" ); document.write( " $\"+s%5B1%5D+=+8W+-+72%2F%28W%5E2%29+\"$
\n" ); document.write( " $\"+8W+-+72%2F%28W%5E2%29+=+0+\"$
\n" ); document.write( " $\"+8W+=+72%2F%28W%5E2%29+\"$
\n" ); document.write( " $\"+W%5E3+=+9+\"$
\n" ); document.write( " $\"+W+=+root%28+3%2C+9+%29+\"$
\n" ); document.write( " $\"+W+=+2.08008+\"$
\n" ); document.write( "height = $\"+2W+=+4.16016+\"$
\n" ); document.write( "length = $\"+L+=+9+%2F+%28W%5E2%29+\"$
\n" ); document.write( "length = $\"+9+%2F+4.32673+\"$
\n" ); document.write( "length = $\"+2.08008+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+2.08008%2A2.08008%2A4.16016+=+18+\"$
\n" ); document.write( " $\"+17.9999+=+18+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Here's a plot of the surface area function,
\n" ); document.write( " $\"+S+\"$ and $\"+W+\"$
\n" ); document.write( "--------------------
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-100%2C+100%2C+4x%5E2+%2B+36%2Fx+%29+\"$
\n" ); document.write( "Hope I got it -definitely get another opinion on this!!! \n" ); document.write( "

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