document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953226>Question 953226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there! I am not very good at math and I have been stuck on this question for 20 minutes now. The question is: calculate the volume of a box to hold a sphere-shaped beaker with a volume of 413cm^3. The second part is : how much space is being occupied by the beaker and how much is being wasted, in percents.<BR>\n" );
document.write( "Thank you so much, I honestly have no idea what to do.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582106 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of a sphere is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bs%5D+=+%284%2F3%29%2Api%2Ar%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bs%5D+=+%284%2F3%29%2Api%2Ar%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "You are given that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bs%5D+=+413+ ALIGN=MIDDLE  ALT=\"+V%5Bs%5D+=+413+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm3<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+413+=+%284%2F3%29%2Ar%5E3+ ALIGN=MIDDLE  ALT=\"+413+=+%284%2F3%29%2Ar%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+ ALIGN=MIDDLE  ALT=\"+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1239+=+4%2Api%2Ar%5E3+ ALIGN=MIDDLE  ALT=\"+1239+=+4%2Api%2Ar%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Api+ ALIGN=MIDDLE  ALT=\"+4%2Api+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+309.75+%2F+pi+=+r%5E3+ ALIGN=MIDDLE  ALT=\"+309.75+%2F+pi+=+r%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E3+=+98.5966+ ALIGN=MIDDLE  ALT=\"+r%5E3+=+98.5966+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+4.6198+ ALIGN=MIDDLE  ALT=\"+r+=+4.6198+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bs%5D+=+%284%2F3%29%2Api%2Ar%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bs%5D+=+%284%2F3%29%2Api%2Ar%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bs%5D+=+%284%2F3%29%2Api%2A4.6198%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bs%5D+=+%284%2F3%29%2Api%2A4.6198%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%28s%29+=+1.333%2A3.14159%2A98.5983+ ALIGN=MIDDLE  ALT=\"+V%28s%29+=+1.333%2A3.14159%2A98.5983+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%28s%29+=+412.997+ ALIGN=MIDDLE  ALT=\"+V%28s%29+=+412.997+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This looks close enough<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "If this sphere is tightly enclosed in a cube,<BR>\n" );
document.write( "the volume of the box is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bc%5D+=++%282r%29%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bc%5D+=++%282r%29%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r+ ALIGN=MIDDLE  ALT=\"+2r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to a side<BR>\n" );
document.write( "of the box<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bc%5D+=+%28+2%2A4.6198+%29%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bc%5D+=+%28+2%2A4.6198+%29%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bc%5D+=+9.2396%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bc%5D+=+9.2396%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bc%5D+=+788.7866+ ALIGN=MIDDLE  ALT=\"+V%5Bc%5D+=+788.7866+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bc%5D+-+V%5Bs%5D+=+788.7866+-+413+ ALIGN=MIDDLE  ALT=\"+V%5Bc%5D+-+V%5Bs%5D+=+788.7866+-+413+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bc%5D+-+V%5Bs%5D+=+375.7866+ ALIGN=MIDDLE  ALT=\"+V%5Bc%5D+-+V%5Bs%5D+=+375.7866+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( wasted volume in cm3 )<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "You are asked for:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+V%5Bc%5D+-+V%5Bs%5D+%29+%2F+V%5Bc%5D+%29%2A100+ ALIGN=MIDDLE  ALT=\"+%28+V%5Bc%5D+-+V%5Bs%5D+%29+%2F+V%5Bc%5D+%29%2A100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a %<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+375.7866+%2F+788.7866+%29%2A100+ ALIGN=MIDDLE  ALT=\"+%28+375.7866+%2F+788.7866+%29%2A100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.4764%2A100+=+47.64+ ALIGN=MIDDLE  ALT=\"+.4764%2A100+=+47.64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "47.64% is wasted space inside the cube<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Hope I got it -tough calculations\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );