document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212578>Question 212578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One cubic millimeter of oil is spread on the surface of the water so that the surface of water so that the oil film has an area of 1 square meter.<BR>\n" );
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document.write( "What is the thickness of the oil film in angstrom units? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160531 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First an Angstrom = 1 ten billionth of a meter.  That is 1/10,000,000,000 of a meter.  (By the way, I didn't know that!  I had to look it up!!)\r<BR>\n" );
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document.write( "The oil is going to form what is essentially a \"cylinder\" as it spreads out in a circle, with a radius, and a VERY small thickness (or height!).  What you want to find is the height of the cylinder, given that the volume is 1 cubic millimeter and the AREA of the circle is 1 square meter.\r<BR>\n" );
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document.write( "The formula for the volume of a cylinder is V = Area * Height.\r<BR>\n" );
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document.write( "In this case, it will be V=Area*Thickness, where V=1 cu mm, A=1 sq m, Thickness = x, the unknown.\r<BR>\n" );
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document.write( "In order to get the same units, convert 1 cu mm to cu m.  First 1 mm = .001 m, so 1 mm^3 = .001^3 m^3.  In scientific notation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%5E-3%29%5E3=10%5E-9 ALIGN=MIDDLE  ALT=\"%2810%5E-3%29%5E3=10%5E-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "V=Area*Thickness<BR>\n" );
document.write( "1 cu mm = 10^-9 cu m = 1 sq m  * x m\r<BR>\n" );
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document.write( "Turn it around!  It will look better:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+sq+m+%2Ax+m+=+10%5E%28-9%29 ALIGN=MIDDLE  ALT=\"1+sq+m+%2Ax+m+=+10%5E%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu m\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+10%5E%28-9%29+ ALIGN=MIDDLE  ALT=\"x=+10%5E%28-9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m   (Square meters divides into cubic meters leaving meters for the correct unit!)\r<BR>\n" );
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document.write( "Now convert this to Angstroms, where 1 Angstrom = 10^-10 meters.  \r<BR>\n" );
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document.write( "Multiply both sides of the above equation by 10:<BR>\n" );
document.write( "10 Angstroms = 10* 10^-10 meters = 10^-9, and that is exactly what you have!\r<BR>\n" );
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document.write( "10 Angstroms should be the final answer.  Wow!  Where did you get THAT problem???  Somebody send me an email if I'm wrong!!\r<BR>\n" );
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document.write( "R^2\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Semi-retired<BR>\n" );
document.write( "Seminole Community College<BR>\n" );
document.write( "Altamonte Springs, FL  32714\r<BR>\n" );
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document.write( "   </SPAN>\n" );
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