document.write( "Question 1208903: Let L = lateral area.\r
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\n" ); document.write( "\n" ); document.write( "Given L = pi•r•sqrt{r^2 + h^2}, solve for h.
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Algebra.Com's Answer #847419 by ikleyn(52863)\"\" \"About 
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\n" ); document.write( "Let L = lateral area  of  a  cone.\r
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\n" ); document.write( "\n" ); document.write( "Given   L = pi•r•sqrt{r^2 + h^2},  solve for  h.
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document.write( "Your starting formula is \r\n" );
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document.write( "    L = \"pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29\".\r\n" );
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document.write( "Divide both sides by \"pi%2Ar\"\r\n" );
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document.write( "    \"L%2F%28pi%2Ar%29\" = \"sqrt%28r%5E2%2Bh%5E2%29\".\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "    \"%28L%2F%28pi%2Ar%29%29%5E2\" = \"r%5E2+%2B+h%5E2\".\r\n" );
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document.write( "Express  \"h%5E2\"\r\n" );
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document.write( "    \"h%5E2\" = \"%28L%2F%28pi%2Ar%29%29%5E2\" - \"r%5E2\"\r\n" );
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document.write( "Take the square root of both sides and use its positive value\r\n" );
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document.write( "    h = \"sqrt%28%28L%2F%28pi%2Ar%29%29%5E2-r%5E2%29\".\r\n" );
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document.write( "It is the desired expression for h.    ANSWER\r\n" );
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