\r\n" );
document.write( "A company that manufactures dog food wishes to pack in closed cylindrical tins.\r\n" );
document.write( "What should be the dimensions of each tin if it is to have a volume of\r\n" );
document.write( "128πcm³ and the minimum possible surface area:\r\n" );
document.write( "\r\n" );
document.write( "In the UK, you say \"tin\". In the US, we say \"can\". LOL \r\n" );
document.write( "\r\n" );
document.write( "The volume of a cylinder is \r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Which simplifies to \r\n" );
document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "The surface area of a cylinder with a top and bottom is\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "Substituting for h:\r\n" );
document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "Differentiating w/r r:\r\n" );
document.write( "
\r\n" );
document.write( "Setting the derivative equal to zero:\r\n" );
document.write( "
\r\n" );
document.write( "Dividing through by -4π\r\n" );
document.write( "
\r\n" );
document.write( "Multiplying through by r2\r\n" );
document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "So the radius of each can should be 4 cm. (diameter = 8 cm.)\r\n" );
document.write( "Substituting in\r\n" );
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document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "And the height of each can should be 8 cm.\r\n" );
document.write( "\r\n" );
document.write( "So the mid-cross section of each can should be an 8 cm x 8 cm square!\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
