document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176844>Question 176844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many faces does a cylinder have?<BR>\n" );
document.write( "Do faces have to be flat?<BR>\n" );
document.write( "Does a sphere have a face?<BR>\n" );
document.write( "Ms. Weaver<BR>\n" );
document.write( "3rd grade teacher </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131914 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Typically, a face is defined as a polygon that is a flat surface of a solid figure.  That means that if we can consider a circle to be a polygon, then a cylinder actually has two faces, namely the circles that form the two bases.  So, the question becomes: Can we consider a circle to be a polygon?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A polygon is a closed plane figure bounded by three or more line segments.  Three or more means that then number of sides can be as large as you like.  A circle is actually the limiting figure for an n-sided polygon as n increases without bound.  In other words, it is perfectly proper to say that a circle is an infinite-sided polygon.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, we have established that faces must be flat and faces must be polygons and that a circle is, in fact, a polygon.  Therefore a right circular cylinder has two faces.  In fact, we can generalize even further to include oblique cylinders and cylinders where the base is elliptical rather than circular.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Given all of that, does a sphere have a face?  No.  And while we are at it, a cone has one face.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );