document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66751>Question 66751</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of sheet metal with an area of 1200 in^2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in^3.  What are the dimensions of the sheet metal?<BR>\n" );
document.write( "I am to come up with a system of equations to solve this problem.  The sides of the rectangle are labeled x and y.  <BR>\n" );
document.write( "I know that {x*y=1200 in^2}; x would be the circumference of the cylinder which would mean that {x=2(PI)r}; the volume would be {(PI)r^2(y)=600 in^3}.  I just can't figure out how to show it all in terms of y and x to figure out the equation.  Thanks.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47403 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=47403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct in what you have done so far.<BR>\n" );
document.write( "Let's start with the volume of the cylindical pipe.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29r%5E2y+=+600 ALIGN=MIDDLE  ALT=\"%28pi%29r%5E2y+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Substitute r here with: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+x%2F2%28pi%29 ALIGN=MIDDLE  ALT=\"r+=+x%2F2%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%28pi%29r ALIGN=MIDDLE  ALT=\"x+=+2%28pi%29r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28x%2F2%28pi%29%29%5E2y+=+600 ALIGN=MIDDLE  ALT=\"%28pi%29%28x%2F2%28pi%29%29%5E2y+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F4%28pi%29%29y+=+600 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F4%28pi%29%29y+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now substitute the y here with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1200%2Fx ALIGN=MIDDLE  ALT=\"y+=+1200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the area, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+=+1200 ALIGN=MIDDLE  ALT=\"xy+=+1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F4%28pi%29%29%281200%2Fx%29+=+600 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F4%28pi%29%29%281200%2Fx%29+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200x%2F4%28pi%29+=+600 ALIGN=MIDDLE  ALT=\"1200x%2F4%28pi%29+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28pi%29 ALIGN=MIDDLE  ALT=\"4%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200x+=+2400%28pi%29 ALIGN=MIDDLE  ALT=\"1200x+=+2400%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 1200.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%28pi%29 ALIGN=MIDDLE  ALT=\"x+=+2%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, from above:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1200%2Fx ALIGN=MIDDLE  ALT=\"y+=+1200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1200%2F2%28pi%29 ALIGN=MIDDLE  ALT=\"y+=+1200%2F2%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+600%2F%28pi%29 ALIGN=MIDDLE  ALT=\"y+=+600%2F%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The dimensions of the rectangular metal sheet are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28pi%29 ALIGN=MIDDLE  ALT=\"2%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F%28pi%29 ALIGN=MIDDLE  ALT=\"600%2F%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches. or...using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29+=+3.14 ALIGN=MIDDLE  ALT=\"%28pi%29+=+3.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > as an approximation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283.14%29 ALIGN=MIDDLE  ALT=\"2%283.14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F3.14 ALIGN=MIDDLE  ALT=\"600%2F3.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 6.28 by 191.08 inches.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );