document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475300>Question 475300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dozen golf balls fit inside the shape of a rectangular prism.  The golf balls are packed tightly together and they touch top, bottom and side of the box.  What percentage of the volume within the box is air?\r<BR>\n" );
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document.write( "I have the answer but have no idea how they arrived at it.<BR>\n" );
document.write( "Air would accupy 47.6 percent of the volume of the box. (100-52.4=47.6)\r<BR>\n" );
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document.write( "How can you get this answer when the question give no numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325909 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=325909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Even though they don't give any numbers, they do give reference points:<BR>\n" );
document.write( "Shape is rectangular prism: Volume = length*width*depth<BR>\n" );
document.write( "Golf balls are like spheres: Volume = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%2Api%2Ar%5E3 ALIGN=MIDDLE  ALT=\"%284%2F3%29%2Api%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Remember the goal isn't to determine the actual volume just comparing the volume the golf balls take up with the volume of the entire box.<BR>\n" );
document.write( "Percentage is just a ratio.<BR>\n" );
document.write( "Now every golf ball is identical in size, so the radius is constant.<BR>\n" );
document.write( "Since we do not know the radius our volumes will be in terms of r.<BR>\n" );
document.write( "The volume of 12 golf balls = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A%284%2F3%29%2Api%2Ar%5E3+=+16%2Api%2Ar%5E3 ALIGN=MIDDLE  ALT=\"12%2A%284%2F3%29%2Api%2Ar%5E3+=+16%2Api%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the tricky part is getting the volume of the box in terms of r.<BR>\n" );
document.write( "Now the dimensions of this box can be anything as long as it holds 12 golf balls perfectly. The easiest thing to do is imagine a long sleeve where all 12 balls are stacked on top of each other. Then it is 12 golf balls high, and length and width is same as length of 1 golf ball. Now remember that length of a circle is the diameter which is twice the radius.<BR>\n" );
document.write( "Now we know the dimensions:<BR>\n" );
document.write( "length = width = 2r<BR>\n" );
document.write( "depth = 12*2r = 24r<BR>\n" );
document.write( "Volume = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%2A2r%2A24r+=+96%2Ar%5E3 ALIGN=MIDDLE  ALT=\"2r%2A2r%2A24r+=+96%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the ratio of golf balls volume to box volume is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2Api%2Ar%5E3%29%2F%2896%2Ar%5E3%29+=+%2816%2Api%29%2F96+=+0.524 ALIGN=MIDDLE  ALT=\"%2816%2Api%2Ar%5E3%29%2F%2896%2Ar%5E3%29+=+%2816%2Api%29%2F96+=+0.524\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So 52.4% of the box is taken up by the golf balls.<BR>\n" );
document.write( "Leaving 47.6% of the box to be taken up by air.<BR>\n" );
document.write( "Hope that helped :) </SPAN>\n" );
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