document.write( "Question 1207300: A company that manufactures dog food wishes to pack in closed cylindrical tins.
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Algebra.Com's Answer #845090 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A company that manufactures dog food wishes to pack in closed cylindrical tin's as,
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document.write( "As you know, the volume of a cylinder is \r\n" );
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document.write( "V = , \r\n" );
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document.write( "where pi = 3.14, r is the radius and h is the height.\r\n" );
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document.write( "In your case the volume is fixed:\r\n" );
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document.write( " =   cm^3.       (1)\r\n" );
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document.write( "The surface area of a cylinder is \r\n" );
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document.write( "S = ,    (2)\r\n" );
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document.write( "and they ask you to find minimum of (2) under the restriction (1).\r\n" );
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document.write( "Using (1), I can rewrite (2) in the form\r\n" );
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document.write( "S(r) =  +  =  +  =  + .   (3)\r\n" );
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document.write( "The plot below shows the function S(r) =  + , and you can clearly see that it has the minimum.\r\n" );
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document.write( "    \r\n" );
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document.write( "        Plot y = \r\n" );
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document.write( "To find the minimum, use Calculus: differentiate the function to get\r\n" );
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document.write( "S'(r) =  +  = \r\n" );
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document.write( "and equate it to zero.\r\n" );
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document.write( "S'(r) = 0   leads you to equation   = ,   which gives \r\n" );
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document.write( "r =  = 4 cm.\r\n" );
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document.write( "Answer.  r = 4 cm, h =  = 8 cm gives the minimum of the surface area.\r\n" );
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