document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142808>Question 1142808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the volume of a pyramid with height of 15 feet and whose base is a square with edges of lengths 10 feet. Show your work using a definite integral.  Check your answer using the formula for the volume of a pyramid.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763543 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "We will integrate in the direction of the height; our \"thin slices\" of the pyramid will be squares whose side length is in constant proportion with the height.<br><BR>\n" );
document.write( "The side of the base is 10 and the height is 15.  That means every cross section will have a side length that is 2/3 of the height at that point.  So if h is the height, <br><BR>\n" );
document.write( "B = ((2/3)h)^2 = (4/9)h^2<br><BR>\n" );
document.write( "Integrate from 0 to 15:<BR>\n" );
document.write( "Integral of ((4/9)h^2dh) = (4/27)h^3 (+C)<br><BR>\n" );
document.write( "The integral evaluated from 0 to 15 is<br><BR>\n" );
document.write( "(4/27)(15^3) = 4(5^3) = 500<br><BR>\n" );
document.write( "The volume of the pyramid by calculus is 500 cubic feet.<br><BR>\n" );
document.write( "By the formula for the volume of a pyramid:<br><BR>\n" );
document.write( "(1/3)(B)(h) = (1/3)(100)(15) = 500<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );