document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119838>Question 119838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can you help me with this problem?\r<BR>\n" );
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document.write( "A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one-third the height of the entire structure. If the total volume of the structure is 2900 ft3 and its radius is 9 ft, what is its height? (Round the answer to one decimal place.)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87842 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one-third the height of the entire structure. If the total volume of the structure is 2900 ft3 and its radius is 9 ft, what is its height? (Round the answer to one decimal place.) <BR>\n" );
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document.write( "Let h = height of the cylindrical section only<BR>\n" );
document.write( "Then<BR>\n" );
document.write( ".5h = height of the conical section only (.5h is 1/3 of 1.5h, the total height)<BR>\n" );
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document.write( "We know:<BR>\n" );
document.write( "vol of a cylinder = pi*r^2*h<BR>\n" );
document.write( "vol of a cone = (1/3)*pi*r^2*h<BR>\n" );
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document.write( "Given:<BR>\n" );
document.write( "Vol of the cylinder + vol of the cone = 2900 cu/ft<BR>\n" );
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document.write( "pi*9^2*h + (1/3*pi*9^2*.5h = 2900<BR>\n" );
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document.write( "pi*81*h + (1/3)*pi*81*.5h = 2900<BR>\n" );
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document.write( "pi*81*h + pi*27*.5h = 2900; took (1/3) of 81<BR>\n" );
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document.write( "254.469h + 42.4115h = 2900<BR>\n" );
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document.write( "296.88h = 2900<BR>\n" );
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document.write( "h = 2900/296.88<BR>\n" );
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document.write( "h = 9.768 ft is the height of the cylinder<BR>\n" );
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document.write( "4.88 ft is the height of the cone<BR>\n" );
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document.write( "9.768 + 4.88 = 14.6 ft is the total height<BR>\n" );
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document.write( "Check solution using 9.8 for ht of the cylinder and 4.9 for the ht of the cone<BR>\n" );
document.write( "pi*9^2*9.8 = 2493.8 cu ft (cylinder)<BR>\n" );
document.write( "(1/3)*pi*9^2*4.9 = 415.6 cu ft (cone)<BR>\n" );
document.write( "2493.8 + 415.6 = 2909.4 ~ 2900 (we rounded both values upward)<BR>\n" );
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document.write( "Did this help? <BR>\n" );
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