document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=612717>Question 612717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I'm here because I need help doing a proof for my geometry class. I need to prove how the volume of a pyramid is 1/3bh. Is there any way you can help me?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385698 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=385698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Most of these proofs require a bit of calculus. If we integrate along the height (h), we can say that the volume V is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V = \int_0^{h} b(\frac{x}{h})^2 dx\"> \r<BR>\n" );
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document.write( "Here, x is a real number which varies between 0 and h. The (x/h)^2 term \"scales\" the area of each cross-section of b. As you can see, if x = 0, the cross-sectional area is 0, if x = h, the cross-sectional area is b.\r<BR>\n" );
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document.write( "Integrating, we obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V = b\frac{x^3}{3h^2}\">. We evaluate at x = h, subtract the value obtained at x = 0:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V = b\frac{h^3}{3h^2} - b\frac{0^3}{3h^2}\">\r<BR>\n" );
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document.write( "Simplifying everything, we obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V = \frac{1}{3}bh\"> </SPAN>\n" );
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