document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83799>Question 83799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you could fill a basketball with root beer, how many cans would it hold?<BR>\n" );
document.write( "(12oz can & regulation NBA ball.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60278 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hmmmm. I wonder if you are doing this as a math exercise or as an actual project. As a <BR>\n" );
document.write( "math exercise you can make certain assumptions that you may not want to make if you are<BR>\n" );
document.write( "performing a \"real world\" measurement.<BR>\n" );
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document.write( "Let's do it as a math exercise first.  The circumference of an NBA basketball is (measured<BR>\n" );
document.write( "in the grooves on the ball) 29.5 inches. Use the formula for circumference to find the radius<BR>\n" );
document.write( "of an NBA basketball:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%2Api%2AR ALIGN=MIDDLE  ALT=\"C+=+2%2Api%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 29.5 inches for the circumference of the ball and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29.5+=+2%2Api%2AR ALIGN=MIDDLE  ALT=\"29.5+=+2%2Api%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for R by dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29.5%2F%282%2Api%29+=+R ALIGN=MIDDLE  ALT=\"29.5%2F%282%2Api%29+=+R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using a calculator to do the math on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+4.695070821 ALIGN=MIDDLE  ALT=\"R+=+4.695070821\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches<BR>\n" );
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document.write( "Now you can find the volume of the basketball by using the formula for the volume of<BR>\n" );
document.write( "a sphere:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%284%2F3%29%2Api%2AR%5E3 ALIGN=MIDDLE  ALT=\"V+=+%284%2F3%29%2Api%2AR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 4.695070821 inches for R and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%284%2F3%29%2Api%2A%284.695070821%29%5E3 ALIGN=MIDDLE  ALT=\"V+=+%284%2F3%29%2Api%2A%284.695070821%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time ... Using a calculator to perform the math on the right side of this equation<BR>\n" );
document.write( "you should find that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+433.5259036 ALIGN=MIDDLE  ALT=\"V+=+433.5259036\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic inches<BR>\n" );
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document.write( "Now assume that 12 oz of root beer is the same volume as 12 oz of water.  At 39.164 degrees<BR>\n" );
document.write( "Fahrenheit water weighs 0.036313 lbs per cubic inch and since a lb is 16 oz, we can multiply<BR>\n" );
document.write( "this figure by 16 to find out that the density of water is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+0.036313%2A16+=+0.581008 ALIGN=MIDDLE  ALT=\"D+=+0.036313%2A16+=+0.581008\"   DISABLED_style= \"max-width:90%; height:auto;\" > ounces per cubic inch. Therefore a 12 oz can contains<BR>\n" );
document.write( "a volume of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F0.581008+=+20.65376036 ALIGN=MIDDLE  ALT=\"12%2F0.581008+=+20.65376036\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic inches.<BR>\n" );
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document.write( "[Just as a sanity check, the approximate dimensions of a 12 oz can are about 1.25 inches <BR>\n" );
document.write( "in radius and 4.5 inches tall to the lid.  This leads to a volume of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A1.25%5E2+%2A4.5+=+22.1 ALIGN=MIDDLE  ALT=\"pi%2A1.25%5E2+%2A4.5+=+22.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic<BR>\n" );
document.write( "inches ... <BR>\n" );
document.write( "pretty close to what we found.]<BR>\n" );
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document.write( "So if a 12 oz can of root beer contains 20.65376036 cubic inches of root beer, we can <BR>\n" );
document.write( "divide this into the volume of the basketball, and find out how many cans the basketball <BR>\n" );
document.write( "can hold.  Recall that the volume of the basketball was 433.5259036 cubic inches. Divide<BR>\n" );
document.write( "that by 20.65376036 cubic inches per can of root beer, and the answer for the number<BR>\n" );
document.write( "of cans of root beer that can be poured into the basketball is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+433.5259036%2F20.65376036+=+20.99016818 ALIGN=MIDDLE  ALT=\"N+=+433.5259036%2F20.65376036+=+20.99016818\"   DISABLED_style= \"max-width:90%; height:auto;\" > or about 21 cans of root beer in the <BR>\n" );
document.write( "basketball.<BR>\n" );
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document.write( "There are a lot of chances for error in this problem.  Recall that we used the outside<BR>\n" );
document.write( "dimensions of the basketball to calculate the interior volume.  This ignores the fact that<BR>\n" );
document.write( "the interior of the basketball will be somewhat smaller because of the thickness of the skin<BR>\n" );
document.write( "that forms the ball.  Also the NBA basketball is allowed to range in circumference<BR>\n" );
document.write( "from 29.5 to 29.75 inches.  So its interior volume can vary somewhat from its size and<BR>\n" );
document.write( "the thickness of the material that comprises. Add to that that the interior volume of<BR>\n" );
document.write( "the basketball is less when the ball is deflated so you can pour root beer into it.<BR>\n" );
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document.write( "Another source of error can come from the fact that we equated ounces of root beer to<BR>\n" );
document.write( "ounces of water.  This is not likely to be true.  A can of root beer will likely sink in water,<BR>\n" );
document.write( "indicating that it is denser than water.  [However, a can of diet root beer may very well<BR>\n" );
document.write( "float because it is likely to be less dense than water.] <BR>\n" );
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document.write( "And finally, the density of water changes slightly with temperature.  The temperature <BR>\n" );
document.write( "of the water we used makes water its most dense.  Warmer than that temperature would<BR>\n" );
document.write( "decrease the density.<BR>\n" );
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document.write( "All these variables would make this an interesting science experiment.  However, the answer<BR>\n" );
document.write( "we came up with is probably pretty close.  <BR>\n" );
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document.write( "Check the math above. It's sort of late to be working math problems, and there's a reasonable<BR>\n" );
document.write( "chance that an error may have crept in somewhere.<BR>\n" );
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document.write( "Hope this helps you to see your way through the problem.<BR>\n" );
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