document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128411>Question 1128411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct a rational function that will help solve the problem. Then, use a calculator to answer the question. \r<BR>\n" );
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document.write( "A right circular cylinder is to have a volume of 45 cubic inches. It costs 4¢/square inch to construct the top and bottom and 1¢/square inch to construct the rest of the cylinder. Find the radius to yield minimum cost. Let x = radius. (Round your answer to two decimal places.)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744873 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=744873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Thank you, but I'll use r for the radius instead of x; that's less confusing.  I can call it x when I put the function in my calculator, since my calculator doesn't recognize the \"r\".<br><BR>\n" );
document.write( "The cost is 4 cents per square inch for the top and bottom and 1 cent per square inch for the sides:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28r%29+=+4%282%28pi%29r%5E2%29%2B1%282%28pi%29rh%29 ALIGN=MIDDLE  ALT=\"C%28r%29+=+4%282%28pi%29r%5E2%29%2B1%282%28pi%29rh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We need the function in terms of a single variable.  To do that, we use the given volume and the formula for the volume to find the height h in terms of r:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+=+%28pi%29r%5E2h ALIGN=MIDDLE  ALT=\"45+=+%28pi%29r%5E2h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+45%2F%28%28pi%29r%5E2%29 ALIGN=MIDDLE  ALT=\"h+=+45%2F%28%28pi%29r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now our cost function is in terms of r only:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28r%29+=+8%28pi%29r%5E2%2B2%28pi%29r%28%2845%29%2F%28%28pi%29r%5E2%29%29+=+8%28pi%29r%5E2%2B90%2Fr ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Put that equation in your graphing calculator, graph it, and find the value of x (r) that gives the minimum function value (minimum cost).<br><BR>\n" );
document.write( "Your graph should look something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-1%2C5%2C-50%2C400%2C8%28pi%29x%5E2%2B90%2Fx%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-1%2C5%2C-50%2C400%2C8%28pi%29x%5E2%2B90%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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