document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099103>Question 1099103</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please solve this question,<BR>\n" );
document.write( "A cube with sides of 6cm is built out of 1 cm cubes. <BR>\n" );
document.write( "The outside of the large cube is painted red.<BR>\n" );
document.write( "How many of the smaller 1cm cubes will have:<BR>\n" );
document.write( "A. 2 faces painted red? -------<BR>\n" );
document.write( "B. 3 faces painted red? -------<BR>\n" );
document.write( "C. No red faces?------<BR>\n" );
document.write( "Reguards<BR>\n" );
document.write( "Raza<BR>\n" );
document.write( "Email. razamuh@hotmail.com  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713589 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=713589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is no need to post your email with the question.<BR>\n" );
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document.write( " <BR>\n" );
document.write( "The big cube has 8 corners.<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > little cubes on those corners will have 3 faces painted.<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "The big cube has 12 edges.<BR>\n" );
document.write( "There are 6 little cubes along each of those edges,<BR>\n" );
document.write( "but the 2 at the ends are on a corner of the big cube.<BR>\n" );
document.write( "We already figured out what happens with those little cubes.<BR>\n" );
document.write( "The little cubes on the big cube's edges that are not on a corner<BR>\n" );
document.write( "will have 2 faces painted.<BR>\n" );
document.write( "There are 6-2=4 such little cubes on each of the 12 edges,<BR>\n" );
document.write( "for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A12=highlight%2848%29 ALIGN=MIDDLE  ALT=\"4%2A12=highlight%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > little cubes with 2 faces painted.<BR>\n" );
document.write( " <BR>\n" );
document.write( "There are also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A4=16 ALIGN=MIDDLE  ALT=\"4%2A4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > little cubes forming the center of each big  cube face<BR>\n" );
document.write( "that will have only one face painted. You did not ask about those, but there are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A16=96 ALIGN=MIDDLE  ALT=\"6%2A16=96\"   DISABLED_style= \"max-width:90%; height:auto;\" > with exactly one face painted.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you peel the outer layer of little cubes, you get a medium sized cube,<BR>\n" );
document.write( "with 4 cm edges made up of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A4%2A4=64 ALIGN=MIDDLE  ALT=\"4%2A4%2A4=64\"   DISABLED_style= \"max-width:90%; height:auto;\" > little cubes.<BR>\n" );
document.write( "Those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2864%29 ALIGN=MIDDLE  ALT=\"highlight%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > little cubes have no face painted.<BR>\n" );
document.write( " <BR>\n" );
document.write( "VERIFICATION:<BR>\n" );
document.write( "aiming up the numbers of little cubes with exactly 0, 1, 2, and 3 faces painted we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2B96%2B48%2B8=216 ALIGN=MIDDLE  ALT=\"64%2B96%2B48%2B8=216\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that makes sense,<BR>\n" );
document.write( "because a big cube with 6 cm edges is made up of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A6%2A6=216 ALIGN=MIDDLE  ALT=\"6%2A6%2A6=216\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "little cubes with 1 cm edges. </SPAN>\n" );
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