document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181950>Question 1181950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A standard beverage can has a volume of 21.7 cubic inches.<BR>\n" );
document.write( "a) Use formula for the volume of cylinder to write an equation that gives the height h of a standard beverage can in terms of its radius (I have solved this and I got h=square root (v/pi r)<BR>\n" );
document.write( "b) Using expression for h from part (a) and the formula for the surface area of a cylinder, write an equation gives the surface area of the beverage can S in terms of only its radius r. (I got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=2pi+r%5E2+%2B+2pi-r+sqrt%28v%2Fpi+r%29 ALIGN=MIDDLE  ALT=\"S=2pi+r%5E2+%2B+2pi-r+sqrt%28v%2Fpi+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) Rewrite the equation for S from part (b) as a quotient of 2 polynomials<BR>\n" );
document.write( "d) Use graphing calculator to find the minimum value of S. What are the dimensions r and h of the can that use least amount of material?<BR>\n" );
document.write( "e) Compare dimensions from part (d) with the actual beverages, which radius= 1.25 inches and height= 4.42 inches<BR>\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 #812491 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your answer to part a is incorrect:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  V\ =\ \pi r^2h\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  h(r,V)\ =\ \frac{V}{\pi r^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large V\"> is given to be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 21.7\ in^3\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  h(r)\ =\ \frac{21.7}{\pi r^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And the height will be in inches because you are dividing cubic inches by square inches.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Part b isn't correct either:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r,h)\ =\ 2\pi r^2\ +\ 2\pi rh\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ 2\pi r^2\ +\ 2\pi r\(\frac{21.7}{\pi r^2}\)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ 2\pi r^2\ +\ \frac{43.4}{r}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Part c: Find a common denominator, in this case, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ 2\pi r^2\ +\ \frac{43.4}{r}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ \frac{2\pi r^3}{r}\ +\ \frac{43.4}{r}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ \frac{2\pi r^3\ +\ 43.4}{r}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(Yes, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> is a monomial, but the monomials are a subset of the polynomials so this works)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Solver92311&illustration_name=SodaCanSurfaceArea.jpg\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The actual minimum radius for the minimum Total Surface Area is approximately 1.512 which results in a height of approximately 3.03 inches.\r<BR>\n" );
document.write( "\n" );
document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Solver92311&illustration_name=darwinfish.jpg\">\r<BR>\n" );
document.write( "\n" );
document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );