document.write( "Question 1011932: 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. (The final answer must not contain any variable other than r. Please show all steps including algebra clearly) \n" ); document.write( "

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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 = ,        (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)\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 = .\r\n" );
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document.write( "This is the required formula.\r\n" );
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