document.write( "Question 1207391: A paper cone of circular base diameter 10cm and height 12cm, is flattened out into the sector of a circle, what is the angle of the sector? \n" ); document.write( "

Algebra.Com's Answer #845270 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A paper cone of circular base diameter 10cm and height 12cm, is flattened out
\n" ); document.write( "into the sector of a circle, what is the angle of the sector?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " This problem is nice.\r
\n" ); document.write( "\n" ); document.write( " Solving it step by step, I will try to explain you why it is so.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "When we flatten out a cone into the sector of a circle,\r\n" );
document.write( "the radius of this circle is the slant height of the cone,\r\n" );
document.write( "while the arc of this sector is the circumference of the base circle of the cone.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we should find the slant height and the circumference of the base circle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The slant height is the hypotenuse of the right triangle, whose legs are\r\n" );
document.write( "the radius of the base circle and the height of the cone.\r\n" );
document.write( "\r\n" );
document.write( "So, in our case, the slant height is  \r\n" );
document.write( "\r\n" );
document.write( "    h =  =  =  =  = 13 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The circumference of the base circle is\r\n" );
document.write( "\r\n" );
document.write( "    C =  =  = 31.4159265 cm  (approximately).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the angle of the sector    is connected with the slant height and the arc length\r\n" );
document.write( "by equation\r\n" );
document.write( "\r\n" );
document.write( "    C = ,  \r\n" );
document.write( "\r\n" );
document.write( "where    is in radians.  Here \"h\"  plays the role of the radius of the arc.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we find\r\n" );
document.write( "\r\n" );
document.write( "     =  =  = 2.416609731 radians.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If you want to have it in degrees, convert radians to degrees\r\n" );
document.write( "\r\n" );
document.write( "     =  =  = 138.4615 degrees (approximately).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The angle of the sector is about 2.416609731 radians or 138.4615 degrees.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved in full.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem is nice, because different conceptions of geometry play together to provide the solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );