document.write( "Question 1156779: A cone of height 12cm has a volume of n cm cubed and a curved surface area of n cm squared. Find the vertical angle of the cone.
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Algebra.Com's Answer #779652 by greenestamps(13198) $\"\"$ $\"About$

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\n" ); document.write( " $\"V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29\"$

\n" ); document.write( " $\"A+=+%28pi%29%28r%29%28l%29\"$ where l is the slant height.

\n" ); document.write( "The volume and the lateral surface area are numerically equal:

\n" ); document.write( " $\"%281%2F3%29%28pi%29%28r%5E2%29%2812%29+=+%28pi%29%28r%29%28l%29\"$
\n" ); document.write( " $\"4r+=+l\"$

\n" ); document.write( "The radius of the cone r and the slant height 4r form a right triangle with the altitude of the cone. The angle in that triangle at the vertex of the cone is half the vertical angle of the cone; the sine of that angle is r/(4r) = 1/4.

\n" ); document.write( "The vertical angle of the cone is

\n" ); document.write( " $\"2%2Asin%5E%28-1%29%281%2F4%29\"$ = approximately 28.955 degrees.

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