document.write( "Question 684171: Given a sphere of radius R, find the radius r and altitude 2h of the right circular cylinder with largest lateral surface area that can be inscribed in the sphere.\r
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Algebra.Com's Answer #424049 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "This is a cross section cut through the center of the sphere:\r\n" );
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document.write( "The lateral area of circular cylinder is\r\n" );
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document.write( "By the Pythagorean theorem (refer to the drawing): , so we substitute:\r\n" );
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document.write( "Since square roots are difficult to work with, let's square both sides:\r\n" );
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document.write( "The trick here is that if we maximize the SQUARE of the lateral area,\r\n" );
document.write( "we will also have maximized the lateral area.  So we let S = A²\r\n" );
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document.write( "We set that equal to zero:\r\n" );
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document.write( "      0 \r\n" );
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document.write( "      0\r\n" );
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document.write( "Divide through by constant \r\n" );
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document.write( "      0\r\n" );
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document.write( "      r=0;         R² - 2r² = 0\r\n" );
document.write( "(min, area = 0)        -2r² = -R²\r\n" );
document.write( "                         r² = \r\n" );
document.write( "                          r =  \r\n" );
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document.write( "So the radius of the cylinder which has maximum\r\n" );
document.write( "surface area is \r\n" );
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document.write( "       Since h = \r\n" );
document.write( "             h = \r\n" );
document.write( "             h = \r\n" );
document.write( "             h = \r\n" );
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document.write( "   height = 2h = \r\n" );
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document.write( "Edwin

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