document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=339398>Question 339398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cone of height 24cm has a curved surface area 550 cm2 . Find its volume </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243216 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Surface area = pi * r^2 + pi * r * sqrt(r^2 + h^2)\r<BR>\n" );
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document.write( "However, we're only finding the area of pi * r * sqrt(r^2 + h^2)\r<BR>\n" );
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document.write( "550 = pi * r * sqrt(r^2 + 24^2)<BR>\n" );
document.write( "550 / pi = r * sqrt(r^2 + 576)<BR>\n" );
document.write( "(550 / pi)^2 = r^2 * (r^2 + 576)<BR>\n" );
document.write( "0 = r^4 + 576 * r^2 - (550 / pi)^2\r<BR>\n" );
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document.write( "t = r^2<BR>\n" );
document.write( "0 = t^2 + 576t - (550 / pi)^2\r<BR>\n" );
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document.write( "t = (-576 +/- sqrt(576^2 + 4 * (550 / pi)^2)) / 2<BR>\n" );
document.write( "We want a positive answer\r<BR>\n" );
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document.write( "t = (-576 + 2 * sqrt(82944 + (550 / pi)^2)) / 2<BR>\n" );
document.write( "t = -288 + sqrt(82944 * pi^2 + 550^2) / pi<BR>\n" );
document.write( "t = -288 + (1/pi) * 1058.8316520788164279747069707806<BR>\n" );
document.write( "t = 49.036582661003100584565681713644<BR>\n" );
document.write( "r^2 = 49.036582661003100584565681713644<BR>\n" );
document.write( "r = 7.0026125596810723871080457785158\r<BR>\n" );
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document.write( "For all intents and purposes, I'm going to presume that the radius of the cone is 7cm. From there, the volume is easy to derive. The volume of ALL right pyramids is:\r<BR>\n" );
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document.write( "(1/3) * B * h\r<BR>\n" );
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document.write( "where B = area of the base\r<BR>\n" );
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document.write( "(1/3) * B * h\r<BR>\n" );
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document.write( "B = pi * r^2<BR>\n" );
document.write( "B = pi * 49\r<BR>\n" );
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document.write( "(1/3) * pi * 49 * 24<BR>\n" );
document.write( "pi * 8 * 49<BR>\n" );
document.write( "pi * 392\r<BR>\n" );
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document.write( "392pi cm^3\r<BR>\n" );
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document.write( "1231.5043202071989494773562062456 cm^3\r<BR>\n" );
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document.write( "It can be rounded to 1232 (cm)^3 as the volume of your cone.<BR>\n" );
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