document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957805>Question 957805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An iron pipe 10 ft. long has an internal diameter of 1 ft. If the iron is 1/2 in. thick, find the volume of metal in the pipe.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585361 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=585361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the metal of the pipe forms a tube and since it is unlikely you have a formula for the volume of a tube, we must find the volume of the tube by adding or subtracting volumes we can find.\r<BR>\n" );
document.write( "\n" );
document.write( "The pipe, with the air inside of it, forms a cylinder. Just the air inside the pipe also forms a cylinder. And there is a well-known formula for the volume of a cylinder:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"V+=+pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The volume of the metal in the pipe, the tube, will be the volume of the pipe and the air minus the volume of the air.<br><BR>\n" );
document.write( "Now we just need to find the values for the volume formula: the radius and hieght of each cylinder. The internal diameter of the pipe is 1 foot. This makes the radius of the air 1/2 feet. The thickness of the pipe is 1/2 inch or 1/24 foot. This makes the radius of the pipe-and-air cylinder:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+%2B+1%2F24+=+12%2F24+%2B+1%2F24+=+13%2F24 ALIGN=MIDDLE  ALT=\"1%2F2+%2B+1%2F24+=+12%2F24+%2B+1%2F24+=+13%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. The height of both cylinders is 10 feet.<br><BR>\n" );
document.write( "Now we can indert these values into our volume formula. For the pipe-and-air cylinder:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2A%2813%2F24%29%5E2%2A10+=+pi%2A%28169%2F576%29%2A10+=+%28845%2F288%29pi ALIGN=MIDDLE  ALT=\"V+=+pi%2A%2813%2F24%29%5E2%2A10+=+pi%2A%28169%2F576%29%2A10+=+%28845%2F288%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu. ft.<br><BR>\n" );
document.write( "For the air-only cylinder:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2A%281%2F2%29%5E2%2A10+=+pi%2A%281%2F4%29%2A10+=+%285%2F2%29pi ALIGN=MIDDLE  ALT=\"V+=+pi%2A%281%2F2%29%5E2%2A10+=+pi%2A%281%2F4%29%2A10+=+%285%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu. ft.<br><BR>\n" );
document.write( "For the volume of the metal of the pipe we subtract these:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28845%2F288%29pi+-+%285%2F2%29pi ALIGN=MIDDLE  ALT=\"V+=+%28845%2F288%29pi+-+%285%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu. ft.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28845%2F288%29pi+-+%28720%2F288%29pi ALIGN=MIDDLE  ALT=\"V+=+%28845%2F288%29pi+-+%28720%2F288%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu. ft.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28125%2F288%29pi ALIGN=MIDDLE  ALT=\"V+=+%28125%2F288%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu. ft.<BR>\n" );
document.write( "This is an exact expression for the volume of the metal of the pipe. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );