document.write( "Question 1085023: The lateral area of a right circular cone is 416.27 cm² .Its altitude is 2/3 of its radius. Determine the radius of the cone. \n" ); document.write( "

Algebra.Com's Answer #699163 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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let r = the radius of the cone
\n" ); document.write( "then
\n" ); document.write( " $\"2%2F3\"$ r = the height of the cone
\n" ); document.write( ":
\n" ); document.write( "Area formula A = $\"pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29\"$
\n" ); document.write( " $\"pi%2Ar%2Asqrt%28r%5E2%2B%28%282%2F3%29r%29%5E2%29\"$ = 416.27
\n" ); document.write( " $\"pi%2Ar%2Asqrt%28r%5E2%2B%284%2F9%29r%5E2%29\"$ = 416.27
\n" ); document.write( " $\"pi%2Ar%2Asqrt%28%2813%2F9%29r%5E2%29\"$ = 416.27
\n" ); document.write( "extract the squares
\n" ); document.write( " $\"%28%28pi%2Ar%5E2%29%2F3%29%2Asqrt%2813%29\"$ = 416.27
\n" ); document.write( "multiply both sides by 3
\n" ); document.write( " $\"pi%2Ar%5E2%2Asqrt%2813%29\"$ = 1248.81
\n" ); document.write( "divide both sides by the sq root of 13
\n" ); document.write( " $\"pi%2Ar%5E2+=+346.3576\"$
\n" ); document.write( "divide both sides by pi
\n" ); document.write( "r^2 = 110.25
\n" ); document.write( "r = $\"sqrt%28110.25%29\"$
\n" ); document.write( "r = 10.5 cm is the radius of the cone
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