document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198595>Question 1198595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, find the total area and volume of the cone. The volume of the solid generated by this triangle may be expressed as V=  βπ/σ  √γ 〖in〗^3 where β and σ are positive integers and γ is a prime number. Find the smallest sum of β, γ, and σ. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837148 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, find the total area and volume of the cone.\r<BR>\n" );
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document.write( "The central angle is 120 deg<BR>\n" );
document.write( "radius = 20 in\r<BR>\n" );
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document.write( "length of arc = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta%2F360 ALIGN=MIDDLE  ALT=\"theta%2F360\"   DISABLED_style= \"max-width:90%; height:auto;\" >*2*pi*r\r<BR>\n" );
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document.write( "= 120/360 *2*20*pi<BR>\n" );
document.write( "=40 *pi/3<BR>\n" );
document.write( "When it is rolled into a cone the radius beomes the slant height and length of arc beomes circumference 0f the base of cone\r<BR>\n" );
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document.write( "2*pi*r = 40 *pi/3<BR>\n" );
document.write( "r = 40/6 =20/3\r<BR>\n" );
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document.write( "height = sqrt(20^2-(20/3)^2 )\r<BR>\n" );
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document.write( "Volume of cone = 1/3  pi*r^2<BR>\n" );
document.write( "height of cone = sqrt(20^2-(20/3)^2)\r<BR>\n" );
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document.write( "height h =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Asqrt%282%29%2F3 ALIGN=MIDDLE  ALT=\"40%2Asqrt%282%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "radius r=20/3<BR>\n" );
document.write( "slant height l=20 <BR>\n" );
document.write( "Find volume and Total surface area\r<BR>\n" );
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