document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193537>Question 193537</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321331793/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A heavy metal sphere with radius 10 cm is dropped into a<BR>\n" );
document.write( "right circular cylinder with base radius of 10 cm. If the<BR>\n" );
document.write( "original cylinder has water in it that is 20 cm high, how<BR>\n" );
document.write( "high is the water after the sphere is placed in it?\r<BR>\n" );
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document.write( "I do not understand how to solve this.  Please help.  Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145278 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=145278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here is a URL for volume --> http://math.about.com/od/formulas/ss/surfaceareavol.htm\r<BR>\n" );
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document.write( "Let's think about this first.<BR>\n" );
document.write( "We have a sphere that will sink in the water.<BR>\n" );
document.write( "The cylinder is wide enough to contain the sphere. (one could argue that a sphere with radius 10 won't fit into a cylinder with radius 10. But we will let that one go for now)\r<BR>\n" );
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document.write( "When we drop the sphere into the cylinder of water, it sinks to the bottom.\r<BR>\n" );
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document.write( "How much water is displaced by the sphere we dropped in?\r<BR>\n" );
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document.write( "The volume of a sphere is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4%2Api%2Ar%5E3%2F3 ALIGN=MIDDLE  ALT=\"V+=+4%2Api%2Ar%5E3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we know how much water is displaced.\r<BR>\n" );
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document.write( "Now that we know the amount of water that 'moved', and we know the container holding that water is a right circular cylinder, all we need to know is the formula for the volume of such a cylinder.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2Ar%5E2+%2A+h+ ALIGN=MIDDLE  ALT=\"V+=+pi%2Ar%5E2+%2A+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can equate those two volumes and solve for h<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2Api+%2A+r%5E3+%2F+3+=+pi+%2A+r%5E2+%2A+h+ ALIGN=MIDDLE  ALT=\"4+%2Api+%2A+r%5E3+%2F+3+=+pi+%2A+r%5E2+%2A+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2A+r+%2F+3+=+h+ ALIGN=MIDDLE  ALT=\"4+%2A+r+%2F+3+=+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We are told r = 10 , so that yields <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+40%2F3 ALIGN=MIDDLE  ALT=\"h+=+40%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.33 ALIGN=MIDDLE  ALT=\"13.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > centimeters  </SPAN>\n" );
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