document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085829>Question 1085829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a right circular cone has an altitude of 18 inches and a radius of 8 inches and is 1/4 filled with water. solve the height of the water </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700178 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If one draws a cone with some water in it, the original radius, 8, and the original height, 18, 8/18, are proportional to the radius of the water level r1 and the height of the water level h1 (similar triangles)<BR>\n" );
document.write( "Volume of the cone is (1/3)*pi*r^2*h=(1/3)*pi*64*18=384 pi<BR>\n" );
document.write( "a quarter full is 96 pi in^3<BR>\n" );
document.write( "the equation of the cone with water only is V=96*pi=(1/3)*pi*r1^2*h1<BR>\n" );
document.write( "we know that 8/18=4/9=r1/h1<BR>\n" );
document.write( "4h1/9=r1<BR>\n" );
document.write( "Cancel the pi, and multiply by 3 to clear the 1/3<BR>\n" );
document.write( "288=r1^2*h1=(4h1/9)^2*h1=(16h1^2/81)*h1<BR>\n" );
document.write( "h1^3=288*81/16=23328/16<BR>\n" );
document.write( "h1=1458^(1/3)=11.34 inches.\r<BR>\n" );
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