document.write( "Question 1011918: A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r. \n" ); document.write( "
Algebra.Com's Answer #627745 by ikleyn(52818)\"\" \"About 
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\n" ); document.write( "A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r.
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document.write( "Volume of a cylinder is \r\n" );
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document.write( "V = \"pi%2Ar%5E2%2Ah\",        (1)\r\n" );
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document.write( "where r is the radius of the cylinder and h is the height of the cylinder.\r\n" );
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document.write( "When cylinder of the radius r is inscribed in a sphere of radius r,\r\n" );
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document.write( "h = \"2%2Asqrt%281-r%5E2%29\"       (2)\r\n" );
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document.write( "(make a sketch and apply the Pythagorean theorem).\r\n" );
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document.write( "Substitute (2) into (1), and you will get\r\n" );
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document.write( "V = \"2%2Api%2Ar%5E2%2Asqrt%281-r%5E2%29\".\r\n" );
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document.write( "This is the required formula.\r\n" );
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\n" ); document.write( "Comment from student: Thanks. Please show me how you derive the height algebraically.
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document.write( "It is not algebraically.\r\n" );
document.write( "It is geometrically.\r\n" );
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document.write( "Make a sketch of the section of the sphere with the cylinder inscribed.\r\n" );
document.write( "Then apply the Pythagorean Theorem.\r\n" );
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document.write( "It is so obvious.\r\n" );
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