document.write( "Question 1136494: A cone of height 9cm has a volume of ncm^3 and curved surface area of ncm^2. Find the vertical angle \n" ); document.write( "

Algebra.Com's Answer #754313 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let r be the radius of the cone. With height 9, the slant height l is then $\"sqrt%28r%5E2%2B81%29\"$ .

\n" ); document.write( "The problem says that, ignoring units, the volume and lateral surface area are the same. So

\n" ); document.write( " $\"%281%2F3%29%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%28r%29%28l%29\"$
\n" ); document.write( " $\"%281%2F3%29%28pi%29%28r%5E2%29%289%29+=+%28pi%29%28r%29%28sqrt%28r%5E2%2B81%29%29\"$
\n" ); document.write( " $\"3r+=+sqrt%28r%5E2%2B81%29\"$
\n" ); document.write( " $\"9r%5E2+=+r%5E2%2B81\"$

\n" ); document.write( "I'm not sure of what your definition of \"vertical angle\" is in this problem. The angle between the base and the slant height of the cone is

\n" ); document.write( " $\"arccos%28r%2Fsqrt%28r%5E2%2B81%29%29+=+arccos%28r%2F%283r%29%29+=+arccos%281%2F3%29\"$

\n" ); document.write( "which is 70.53 degrees, to 2 decimal places. \n" ); document.write( "

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