document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173726>Question 1173726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a cylinder just fits into a cube of side length 36m calculate the precentage of empty space in the box </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799003 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The edge of the cube is 36; the volume of the cube is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E3+=+36%5E3 ALIGN=MIDDLE  ALT=\"e%5E3+=+36%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the cylinder just fits inside the cube, its height is 36 and its radius is 18; its volume is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%2818%5E2%29%2836%29 ALIGN=MIDDLE  ALT=\"%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%2818%5E2%29%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The volume of empty space is the difference between the two volumes; the percentage of empty space is the ratio of the volume of empty space to the volume of the cube.<br><BR>\n" );
document.write( "You can do the calculations....<br><BR>\n" );
document.write( "Note that the heights of the cube and cylinder are the same; so the ratio of volumes of the two solids is the same as the ratio of the cross sections of the two solids, which is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28pi%29%28%2836%2F2%29%5E2%29%29%2F%2836%5E2%29+=+pi%2F4 ALIGN=MIDDLE  ALT=\"%28%28pi%29%28%2836%2F2%29%5E2%29%29%2F%2836%5E2%29+=+pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the percentage of empty space is the ratio<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-pi%2F4%29 ALIGN=MIDDLE  ALT=\"%281-pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "converted to a percentage.<br><BR>\n" );
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