document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139193>Question 139193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How is the formula for volume of a prism like the formula for volume of a pyramid? How are they different? Help Please Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101497 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for the volume of a prism is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=Bh ALIGN=MIDDLE  ALT=\"V=Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the area of the base and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height.\r<BR>\n" );
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document.write( "The formula for the volume of a pyramid is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%28Bh%29%2F3 ALIGN=MIDDLE  ALT=\"V=%28Bh%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the area of the base and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height.\r<BR>\n" );
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document.write( "So a pyramid with a base equal in area to a prism and a height equal to the height of the prism has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > the volume.  Notice that the bases don't necessisarily have to have the same shape -- just the same area.  For example, if you had a prism with a triangular base where the base of the triangle was 2 and the altitude of the triangle was 1 and further the height of the prism was 5, then a square based pyramid with sides on the base of 1 unit and a height of 5 would have exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > the volume of the prism.\r<BR>\n" );
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document.write( "By the way, this same relationship holds between a cylinder and a cone.  Equal base areas and equal heights implies a 3 to 1 ratio in the volumes.  That makes perfectly good sense if you consider that a cone is just a pyramid with an infinite number of infinitessimally thin faces, and a cylinder is a prism with an infinite number of infinitessimally thin faces.\r<BR>\n" );
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document.write( "My 5th grade teacher (more years ago than I care to reveal) demonstrated this relationship.  She had a set of clear plastic geometric solids.  She filled the pyramid with sand three times and it filled the equal-based, equal-height prism exactly. </SPAN>\n" );
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