document.write( "Question 1120368: A rectangular piece of sheet metal with an area of 800 in2 is to be bent into a cylindrical length of stovepipe having a volume of 400 in3. What are the dimensions of the sheet metal? (Round your answer to one decimal place.) \r
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Algebra.Com's Answer #736057 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let the dimensions of the rectangular piece be x and y,\r\n" );
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document.write( "    where y be the height of the cylinder.\r\n" );
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document.write( "    (Hence, x is the dimension to be bent into circle/cylinder).\r\n" );
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document.write( "Then we have  FIRST EQUATION  for the original area of the piece \r\n" );
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document.write( "    xy = 800     (1)     (square inches)\r\n" );
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document.write( "When the dimension \"x\" is bent to the circle (to the cylinder latent surface), its radius becomes  r = .\r\n" );
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document.write( "Then the volume of the cylinder is  \r\n" );
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document.write( "    V =  =  =  =    cubic inches,\r\n" );
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document.write( "therefore our  SECOND EQUATION is\r\n" );
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document.write( "     = 400,     (2)       \r\n" );
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document.write( "or\r\n" );
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document.write( "      = .     (2').\r\n" );
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document.write( "Thus we have the system of two equations\r\n" );
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document.write( "     xy = 800,          (1)\r\n" );
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document.write( "      = .    (2')\r\n" );
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document.write( "In  (2')  replace  xy  by  800,  based on (1).  You will get\r\n" );
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document.write( "      = ,    or\r\n" );
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document.write( "     x = .\r\n" );
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document.write( "Thus you solved for x.  Now substitute  x =   into (1) to get\r\n" );
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document.write( "      = 800.\r\n" );
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document.write( "Then you get  y =  = .\r\n" );
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document.write( "Answer.   x =  inches;   y =  inches.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be aware: the system written by @josgarithmetic in his post\r
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\n" ); document.write( "\n" ); document.write( " $\"system%28xy=800%2Cy%2A%28pi%2Ax%5E2%29=400%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "is I N C O R R E C T !\r
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\n" ); document.write( "\n" ); document.write( "For your safety, simply ignore it !\r
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