document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160373>Question 160373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is on solving a word problem. I dont if you can help but this is the problem:\r<BR>\n" );
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document.write( " aA vertical cylindrical storage tank, with diameter 20 feet, is filled with oil to a depth of 40 feet.  Sometime later, the oil is drained, decreasing the deptht a rate of 8 inches per hour.  Write an equation for the volume of oil (ft^3) remaining in the tank t hours later as a function of t.  Draw a geometrically correct sketch, supporting your solution.\r<BR>\n" );
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document.write( "The only thing i can pull out of this problem is that the volume of a cylinder is V = &#960;r^2h. If you could help it would be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118412 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=118412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A vertical cylindrical storage tank, with diameter 20 feet, is filled with oil<BR>\n" );
document.write( " to a depth of 40 feet.  Sometime later, the oil is drained, decreasing the<BR>\n" );
document.write( " depth a rate of 8 inches per hour.  Write an equation for the volume of oil<BR>\n" );
document.write( " (ft^3) remaining in the tank t hours later as a function of t.<BR>\n" );
document.write( "  Draw a geometrically correct sketch, supporting your solution.<BR>\n" );
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document.write( "This is a linear equation so we can find the slope using the time/volume<BR>\n" );
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document.write( "Find the volume at 40 ft, (radius = 10 ft)<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A10%5E2%2A40 ALIGN=MIDDLE  ALT=\"pi%2A10%5E2%2A40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V = 12566 cu ft (rounded to nearest cu ft)<BR>\n" );
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document.write( "Therefore: t=0; v=12566<BR>\n" );
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document.write( "Find out how many hours to empty the tank<BR>\n" );
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document.write( "At 8 in/hr how long to lower it 40 ft?<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2840%2A12%29%29%2F8 ALIGN=MIDDLE  ALT=\"%28%2840%2A12%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 60 hrs (vol = 0)<BR>\n" );
document.write( "Therefore: t=60; v=0<BR>\n" );
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document.write( "Find the slope: m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%280+-+12566%29%29%2F%28%2860-0%29%29 ALIGN=MIDDLE  ALT=\"%28%280+-+12566%29%29%2F%28%2860-0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12566%2F60 ALIGN=MIDDLE  ALT=\"-12566%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope<BR>\n" );
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document.write( "An equation: V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12566%2F60 ALIGN=MIDDLE  ALT=\"-12566%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >t + 12566<BR>\n" );
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document.write( "You can illustrate this with a graph. V = vertical axis; t = horizontal axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+80%2C+-5000%2C+15000%2C+%28-12566%2F60%29x%2B12566%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+80%2C+-5000%2C+15000%2C+%28-12566%2F60%29x%2B12566%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can prove this:<BR>\n" );
document.write( "t = 30 hr<BR>\n" );
document.write( "At 30 hrs the depth would be 30*8\" = 240\" = 20 feet (40-20)<BR>\n" );
document.write( "Find the volume at 20ft<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A10%5E2%2A20 ALIGN=MIDDLE  ALT=\"pi%2A10%5E2%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V = 6283 cu ft <BR>\n" );
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document.write( "Using the equation/graph<BR>\n" );
document.write( "v = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12566%2F60 ALIGN=MIDDLE  ALT=\"-12566%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >(30) + 12566<BR>\n" );
document.write( "v = 6283 cu ft<BR>\n" );
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document.write( "Did this sense to you? I am not sure what kind of sketch they have in mind, I'll<BR>\n" );
document.write( "leave that up to you. </SPAN>\n" );
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