document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95073>Question 95073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is $4.00, while the cylindrical part costs $2.00 per square foot. If the tank needs to hold 10(pi symbol)ft^3 of propane gas, what dimensions minimize the cost of construction? What is the minimum cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69165 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is $4.00, while the cylindrical part costs $2.00 per square foot. If the tank needs to hold 10(pi symbol)ft^3 of propane gas, what dimensions minimize the cost of construction? What is the minimum cost?<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Let the radius be \"x\" feet.<BR>\n" );
document.write( "Area of the combined semi-circular end pieces = 4pir^2 = 4(pi)x^2<BR>\n" );
document.write( "Volume of the combined semi-circular end pieces = (4/3)(pi)x^3<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Area of the cylindrical part = 2(pi)xh<BR>\n" );
document.write( "Volume of the cylindrical part = (pi)x^2h<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "volumn + volumn = volumn<BR>\n" );
document.write( "(4/3)(pi)x^3 + (pi)x^2h = 10(pi)<BR>\n" );
document.write( "(4/3)x^3 + x^2h - 10 = 0<BR>\n" );
document.write( "Comment: Not knowing \"h\" results in not knowing \"x\".<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Price equation:<BR>\n" );
document.write( "price + price = total price<BR>\n" );
document.write( "4[4(pi)x^2] + 2[2(pi)xh] = total price<BR>\n" );
document.write( "Comment: Not knowing \"h\" results in not being able to find the minimum here.<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );