document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011125>Question 1011125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the length of the longest pole that can be put into a room of dimensions 10m×10m×5m. also find the volume of the pole if its radius is 70cm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626705 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=626705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The room, with the pole, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28AC%29 ALIGN=MIDDLE  ALT=\"red%28AC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the pole's shadow, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28AB%29 ALIGN=MIDDLE  ALT=\"blue%28AB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C300%2C-2%2C18%2C-2%2C13%2C%0D%0Arectangle%280%2C0%2C10%2C5%29%2C%0D%0Arectangle%287%2C6%2C16%2C10.5%29%2C%0D%0Aline%2810%2C5%2C16%2C10.5%29%2Cline%2810%2C0%2C16%2C6%29%2C%0D%0Aline%280%2C5%2C7%2C10.5%29%2Cgreen%28line%280%2C0%2C7%2C6%29%29%2C%0D%0Agreen%28line%287%2C10.5%2C7%2C6%29%29%2Cgreen%28line%2816%2C6%2C7%2C6%29%29%2C%0D%0Ablue%28line%2816%2C6%2C0%2C0%29%29%2Clocate%288%2C3.2%2Cblue%28s%29%29%2C%0D%0Ared%28line%280%2C0%2C16%2C10.5%29%29%2Clocate%288.7%2C6%2Cred%28p%29%29%2C%0D%0Alocate%28-0.2%2C0%2CA%29%2Clocate%2816%2C6%2CB%29%2Clocate%2816%2C11.5%2CC%29%2C%0D%0Alocate%284.5%2C0%2C10%29%2Clocate%2813%2C3%2C10%29%2Clocate%2816.1%2C9%2C5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28s%29 ALIGN=MIDDLE  ALT=\"blue%28s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=length of AB, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28p%29 ALIGN=MIDDLE  ALT=\"red%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=length of AB, both in meters.<BR>\n" );
document.write( "On the floor of the room, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28s%29 ALIGN=MIDDLE  ALT=\"blue%28s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the diagonal of a 10m×10m square<BR>\n" );
document.write( "(or the hypotenuse of a right triangle with legs measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10m ALIGN=MIDDLE  ALT=\"10m\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the Pythagorean theorem tells us that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28blue%28s%29%29%5E2=10%5E2%2B10%5E2=200 ALIGN=MIDDLE  ALT=\"%28blue%28s%29%29%5E2=10%5E2%2B10%5E2=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "On an imaginary vertical plane, triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a right triangle,<BR>\n" );
document.write( "and its legs' length, in meters, are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28s%29 ALIGN=MIDDLE  ALT=\"blue%28s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the length, in meters, of hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28p%29=sqrt%28%28blue%28s%29%29%5E2%2B5%5E2%29=sqrt%28200%2B25%29=sqrt%28225%29=highlight%2815%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the length of the longest pole that can be put into a room of dimensions 10m×10m×5m,<BR>\n" );
document.write( "provided that the pole is pencil-thin or thinner.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the pole is wider than pencil-thin its ends will not go all the way into corners <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > , =<BR>\n" );
document.write( "so it would need to be a bit shorter,<BR>\n" );
document.write( "but I do not think that you are expected to do real world calculations,<BR>\n" );
document.write( "as an engineer would do,<BR>\n" );
document.write( "so the expected answer to the second question is the volume of a pole/cylinder<BR>\n" );
document.write( "that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15m ALIGN=MIDDLE  ALT=\"15m\"   DISABLED_style= \"max-width:90%; height:auto;\" > long and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7m=70cm ALIGN=MIDDLE  ALT=\"0.7m=70cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > in radius.<BR>\n" );
document.write( "For a cylinder of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > and height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the volume is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Volume=pi%2AR%5E2%2AL ALIGN=MIDDLE  ALT=\"Volume=pi%2AR%5E2%2AL\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so for your problem, the volume of the pole in cubic meters is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Volume=pi%2A0.7%5E2%2A15=7.35pi ALIGN=MIDDLE  ALT=\"Volume=pi%2A0.7%5E2%2A15=7.35pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2823.09m%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%2823.09m%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );