document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967594>Question 967594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would a tank that has a volume of approximately 150 litres and a maximum length of 1.30m be? show all calculations, lengths, and angles that any lines make to the horizontal.\r<BR>\n" );
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document.write( "the tank that i have designed has the same 'shape' on either end, and a uniform cross-section. the angled lines have different lengths <BR>\n" );
document.write( "I must show my use of trigonometry of how i came up with my final design and i need help with this.<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591449 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=591449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From your description, I do not get the exact idea of what your design is.<BR>\n" );
document.write( "However, I may be able to guess something similar, and the explanation of my calculations could be useful to you.<BR>\n" );
document.write( "A uniform cross-section would mean a cylinder of a right rectangular prism, but those shapes are rather boring, and do not show use of trigonometry.<BR>\n" );
document.write( "I suspect your design is a cylinder with pointy ends added, something that from the side looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28440%2C200%2C-1%2C10%2C-3%2C2%2C%0D%0Aline%280%2C0%2C2%2C-2%29%2Cline%280%2C0%2C2%2C1%29%2C%0D%0Aline%282%2C1%2C7%2C1%29%2Cline%282%2C-2%2C7%2C-2%29%2C%0D%0Aline%287%2C1%2C9%2C0%29%2Cline%289%2C0%2C7%2C-2%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , end on looks like this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-3%2C2%2C-3%2C2%2Ccircle%280%2C-0.5%2C1.5%29%2C%0D%0Acircle%280%2C0%2C0.1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and from the top looks like this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28440%2C200%2C-1%2C10%2C-3%2C2%2C%0D%0Aline%280%2C0%2C2%2C-1.5%29%2Cline%280%2C0%2C2%2C1.5%29%2C%0D%0Aline%282%2C1.5%2C7%2C1.5%29%2Cline%282%2C-1.5%2C7%2C-1.5%29%2C%0D%0Aline%287%2C-1.5%2C9%2C0%29%2Cline%287%2C1.5%2C9%2C0%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You do not need trigonometry for that, unless you care about the exact angles at the pointy ends.<BR>\n" );
document.write( "In my drawing, if we call the diameter of the cylindrical part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=2R ALIGN=MIDDLE  ALT=\"D=2R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >= radius),<BR>\n" );
document.write( "the pointy ends are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29D=%284%2F3%29R ALIGN=MIDDLE  ALT=\"%282%2F3%29D=%284%2F3%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" > up from the bottom (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29D ALIGN=MIDDLE  ALT=\"%281%2F3%29D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the top),<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29D=%284%2F3%29R ALIGN=MIDDLE  ALT=\"%282%2F3%29D=%284%2F3%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" > away from the of end<BR>\n" );
document.write( "of the cylindrical part.<BR>\n" );
document.write( "That makes for a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5Eo ALIGN=MIDDLE  ALT=\"45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > upslope,<BR>\n" );
document.write( "and a downslope with an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=%28%281%2F3%29D%29%2F%28%282%2F3%29D%29=1%2F2 ALIGN=MIDDLE  ALT=\"tan%28theta%29=%28%281%2F3%29D%29%2F%28%282%2F3%29D%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=about26.6%5Eo ALIGN=MIDDLE  ALT=\"theta=about26.6%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It also makes that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29D=%284%2F3%29R%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29D=%284%2F3%29R%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > away from the of cylinder end distance the height of the cone.<BR>\n" );
document.write( "Also, in my drawing, the length of the cylindrical part is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%285%2F3%29D=%2810%2F3%29R ALIGN=MIDDLE  ALT=\"L=%285%2F3%29D=%2810%2F3%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28440%2C200%2C-1%2C10%2C-3%2C2%2C%0D%0Aline%280%2C0%2C2%2C-2%29%2Cline%280%2C0%2C2%2C1%29%2C%0D%0Aline%282%2C1%2C7%2C1%29%2Cline%282%2C-2%2C7%2C-2%29%2C%0D%0Aline%287%2C1%2C9%2C0%29%2Cline%289%2C0%2C7%2C-2%29%2C%0D%0Agreen%28rectangle%287%2C-2%2C9%2C1%29%29%2C%0D%0Alocate%287.1%2C-0.3%2Cgreen%28D%29%29%2Clocate%289.1%2C1%2Cgreen%28%281%2F3%29D%29%29%2C%0D%0Alocate%287.8%2C-2%2Cgreen%28%282%2F3%29D%29%29%2Clocate%289.1%2C-0.9%2Cgreen%28%282%2F3%29D%29%29%2C%0D%0Alocate%283%2C-2%2CL=%285%2F3%29D%29%2Cgreen%28arrow%289%2C0%2C12%2C0%29%29%2C%0D%0Ared%28arc%287%2C1%2C2%2C2%2C0%2C26.6%29%29locate%288%2C0.9%2Cred%28theta%29%29%2C%0D%0Ared%28arc%287%2C-2%2C2%2C2%2C-45%2C0%29%29%2Clocate%288%2C-1.3%2Cred%2845%5Eo%29%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cross section of the cylindrical part (and the bases of the cones)<BR>\n" );
document.write( "are circles 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;\" > ,<BR>\n" );
document.write( "and each has a surface of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2AR%5E2 ALIGN=MIDDLE  ALT=\"pi%2AR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The volume of the cylindrical part would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bcyl%5D=pi%2AR%5E2%2AL=pi%2AR%5E2%2A%2810%2F3%29R=pi%2A%2810%2F3%29%2AR%5E3 ALIGN=MIDDLE  ALT=\"V%5Bcyl%5D=pi%2AR%5E2%2AL=pi%2AR%5E2%2A%2810%2F3%29R=pi%2A%2810%2F3%29%2AR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The volume of a cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the surface area of the base, times the height.<BR>\n" );
document.write( "(It does not matter if it is a right cone,<BR>\n" );
document.write( "with the vertex right above the center of the base)<BR>\n" );
document.write( "or an oblique cone, like those in my design,<BR>\n" );
document.write( "with the vertex not directly above the center of the base).<BR>\n" );
document.write( "So the volume of each conical end is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bcone%5D=%281%2F3%29%2Api%2AR%5E2%2A%284%2F3%29%2AR=%284%2F9%29%2Api%2AR%2A3 ALIGN=MIDDLE  ALT=\"V%5Bcone%5D=%281%2F3%29%2Api%2AR%5E2%2A%284%2F3%29%2AR=%284%2F9%29%2Api%2AR%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The total volume of my tank is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2A%2810%2F3%29%2AR%5E3%2B2pi%284%2F9%29R%5E3%0D%0A=pi%2810%2F3%2B8%2F9%29R%5E3=pi%2830%2F9%2B8%2F9%29R%5E3=pi%2838%2F9%29%2AR%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Considering that 1 liter is 1 cubic decimeter, or 1000 cubic centimeters, for exactly 150 L, I need<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2838%2F9%29%2AR%5E3=150000cm%5E3 ALIGN=MIDDLE  ALT=\"pi%2838%2F9%29%2AR%5E3=150000cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E3=150000%2A9%2F%2838pi%29 ALIGN=MIDDLE  ALT=\"R%5E3=150000%2A9%2F%2838pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E3 ALIGN=MIDDLE  ALT=\"cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=11308.37754cm%5E3 ALIGN=MIDDLE  ALT=\"R%5E2=11308.37754cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=about22.44cm ALIGN=MIDDLE  ALT=\"R=about22.44cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If I use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=22.44cm ALIGN=MIDDLE  ALT=\"R=22.44cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > , my cylinder will have that radius,<BR>\n" );
document.write( "The length will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%2810%2F3%29R=%2810%2F3%29%2A22.44cm=74.82cm=0.7482m ALIGN=MIDDLE  ALT=\"L=%2810%2F3%29R=%2810%2F3%29%2A22.44cm=74.82cm=0.7482m\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the height of each cone end section will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29R=%284%2F3%2922.44cm=29.92cm ALIGN=MIDDLE  ALT=\"%284%2F3%29R=%284%2F3%2922.44cm=29.92cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );