document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108536>Question 1108536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cube of side length s sits inside a sphere of radius r so that the vertices of the cube sit on the sphere. Find the ratio r : s. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723610 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=723610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us pretend that this sketch really looks like the cube <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-6%2C4%2C-0.5%2C9.5%2C%0D%0Aline%280%2C0%2C-5%2C0%29%2Cline%280%2C5%2C-5%2C5%29%2C%0D%0Aline%280%2C0%2C0%2C5%29%2Cline%28-5%2C5%2C-5%2C0%29%2C%0D%0Aline%280%2C0%2C2.4%2C3.2%29%2Cline%280%2C5%2C2.4%2C8.2%29%2C%0D%0Aline%282.4%2C8.2%2C2.4%2C3.2%29%2Cline%28-5%2C5%2C-2.4%2C8.2%29%2C%0D%0Aline%282.4%2C8.2%2C-2.4%2C8.2%29%2Clocate%28-4.9%2C5%2CA%29%2C%0D%0Alocate%28-0.3%2C5%2CB%29%2Clocate%28-0.3%2C0.4%2CC%29%2C%0D%0Alocate%28-4.9%2C0.4%2CD%29%2Clocate%28-2.5%2C8.6%2CE%29%2C%0D%0Alocate%282.3%2C8.6%2CF%29%2Clocate%282.5%2C3.4%2CG%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The seven visible vertices are labeled A through G.<BR>\n" );
document.write( "Vertex H is in back. In the attempted perspective view,<BR>\n" );
document.write( "H is directly behind D, and directly below E.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=AB=BC=CD=DG=FG=AE ALIGN=MIDDLE  ALT=\"s=AB=BC=CD=DG=FG=AE\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of a side of the cube.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AE=sqrt%28s%5E2%2Bs%5E2%29=sqrt%282%29s ALIGN=MIDDLE  ALT=\"AE=sqrt%28s%5E2%2Bs%5E2%29=sqrt%282%29s\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the diagonal of a cube face.<BR>\n" );
document.write( "A cross-section (cutting through A, F, G, and D, would look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C280%2C-0.85%2C9.15%2C-1%2C6%2C%0D%0Agreen%28triangle%280%2C0%2C8.66%2C0%2C8.66%2C5%29%29%2C%0D%0Agreen%28rectangle%288.66%2C0%2C8.36%2C0.3%29%29%2C%0D%0Aline%280%2C0%2C8.66%2CO%29%2Cline%280%2C5%2C8.66%2C5%29%2C%0D%0Aline%280%2C0%2C0%2C5%29%2Cline%288.66%2C0%2C8.66%2C5%29%2C%0D%0Alocate%28-0.1%2C0%2CD%29%2Clocate%288.56%2C0%2CG%29%2C%0D%0Alocate%28-0.1%2C5.4%2CA%29%2Clocate%288.56%2C5.4%2CF%29%2C%0D%0Alocate%284.1%2C0.5%2Csqrt%282%29s%29%2Clocate%288.4%2C2.7%2Cs%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DF=sqrt%28%28sqrt%282%29s%29%5E2%2Bs%5E2%29=sqrt%282s%5E2%2Bs%5E3%29=sqrt%283s%5E2%29=sqrt%283%29s ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the diagonal of the cube,<BR>\n" );
document.write( "the longest possible distance between two points of the cube.<BR>\n" );
document.write( "For the cube to fit in the sphere, that has to be the diameter of the sphere.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r=sqrt%283%29s ALIGN=MIDDLE  ALT=\"2r=sqrt%283%29s\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r%2Fs=sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28r%2Fs=sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The ratio r:s is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (about 0.866). </SPAN>\n" );
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