document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253845>Question 253845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The interior dimensions of a carton in the shape of a rectangular prism are<BR>\n" );
document.write( "2 ft by 1ft by 1 1/2 feet.\r<BR>\n" );
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document.write( "How many boxes, each in the shape of a cube with 1-inch edges, will fit inside<BR>\n" );
document.write( "the carton?\r<BR>\n" );
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document.write( "I think the answer is 36 cubes, but I want to make sure.\r<BR>\n" );
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document.write( "the volume = lxwxh, so the volume would be 3 cubic feet.  Then I thought that<BR>\n" );
document.write( "there would be 36 inches in 3 feet so maybe the answer was 36 cubes.      </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186201 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 feet by 1 foot by 1.5 feet = 24 inches by 12 inches by 18 inches.<BR>\n" );
document.write( "volume of the carton is 24*12*18 = 5184 cubic inches.\r<BR>\n" );
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document.write( "each smaller box is 1 cubic inch (1*1*1).\r<BR>\n" );
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document.write( "24 cubes can fit along the 24 inch side.<BR>\n" );
document.write( "18 cubes can fit along the 18 inch side.<BR>\n" );
document.write( "assuming the height is 12 inches, then 12 cubes high.\r<BR>\n" );
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document.write( "on the bottom of the box, we have 18 rows of 24 cubes each.<BR>\n" );
document.write( "that's 18*24 = 432 cubes on the first inch of height.<BR>\n" );
document.write( "there are 11 more inches of height which makes 11 * 432 = 4752 cubes.<BR>\n" );
document.write( "4752 + 432 = 5184 cubes in total.\r<BR>\n" );
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document.write( "the dimensions of the large carton were in feet.\r<BR>\n" );
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document.write( "you needed to convert them to inches.\r<BR>\n" );
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document.write( "there are 12*12*12 cubic inches in a cubic foot.\r<BR>\n" );
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document.write( "that equals 1728 cubic inches per cubic foot.\r<BR>\n" );
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document.write( "3 * 1728 = 5184 cubic inches which is the same as I calculated earlier.\r<BR>\n" );
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document.write( "each smaller box is 1x1x1 = 1 cubic inches indicating that 5184 of the smaller boxes should fit into the larger carton unless there's some dead space where a smaller cube won't fit.   There was none, so 5184 smaller boxes fit into the larger carton.\r<BR>\n" );
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