document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61016>Question 61016</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0340813970/algebrahomeworkh>as pure mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> a cylindrical tin of particular volume is to be made using as little material as possible. find the ratio of the height to the radius(the tin is closed both ends) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42024 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a cylindrical tin of particular volume is to be made using as little material as possible. find the ratio of the height to the radius(the tin is closed both ends)<BR>\n" );
document.write( "LET THE RATIO OF HEIGHT TO RADIUS = X =H/R.....H=RX<BR>\n" );
document.write( "VOLUME OF CYLINDER = PI*(R^2)*H = V = CONSTANT.<BR>\n" );
document.write( "V = PI*R^2*RX = PI*(R^3)*X<BR>\n" );
document.write( "R=[V/(PI*X)]^(1/3)<BR>\n" );
document.write( "A = AREA OF CYLINDER = 2PI*R*H+2PI*R^2=2PI*R[RX+R]=2PI*(R^2)[X+1]<BR>\n" );
document.write( "A = 2PI*R^2[X+1]=2PI[X+1][V/(PI*X)]^(2/3)<BR>\n" );
document.write( "A=[2PI*V^(2/3)/{PI}^(2/3)][(X+1)/X^(2/3)]<BR>\n" );
document.write( "A = K[X^(1/3)+X^(-2/3)]<BR>\n" );
document.write( "DA/DX = 0 FOR MINIMUM VALUE = K[(1/3){X^(-2/3)} -(2/3){X^(-5/3)}]=0<BR>\n" );
document.write( "1/3{X^(2/3)}= 2/3{X^(5/3)}<BR>\n" );
document.write( "X^(5/3)/X^(2/3)=2<BR>\n" );
document.write( "X = 2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );