document.write( "Question 1183412: A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm. The remaining part is folded to form a cone. Find 1. the vertical angle of the cone 2. The angle of the sector.
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Algebra.Com's Answer #853562 by ikleyn(53575) $\"\"$ $\"About$

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\n" ); document.write( "A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm.
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document.write( "After cutting away the sector of 110°, the remaining pert of the circle is the sector of 360° - 110° = 250°.\r\n" );
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document.write( "The length of the arc of the sector of (250°, R = 70 cm) is\r\n" );
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document.write( "     =  = 305.4323611 cm.\r\n" );
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document.write( "The radius of the base of the cone 'r' can be defined from\r\n" );
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document.write( "     = 305.4323611,  r =  = 48.61111... cm.\r\n" );
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document.write( "It is the same as to use equation\r\n" );
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document.write( "     = ,  r =  =  = 48.61111... cm.\r\n" );
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document.write( "Now the cone has the slant height of 70 cm and the radius of 48.61111... cm.\r\n" );
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document.write( "From the right-angled triangle,  for the angle 'a' between the slant height and the cone axis we have\r\n" );
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document.write( "    sin(a) =  = 0.694444...\r\n" );
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document.write( "Thus angle 'a' is  a = arcsin(0.694444),  or about 44°.\r\n" );
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document.write( "Vertical angle of the cone is about  2*44° = 88°.\r\n" );
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