document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936259>Question 936259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In Egypt four square pyramids. The main pyramid is the tallest, while the other three pyramids each is half of its height. All four pyramids must have a height to base length ratio of 2:3. A maximum amount of 30 million cubic feet of stone allocated for construction.<BR>\n" );
document.write( "Question: Find the largest possible values for the base length and height, to the nearest foot , as well as the volume of each pyramid ,in scientific notation to 3 Decimal places. (volume of pyramid is V= 1/3 Bh ,where B is the area of the base and h is the height.<BR>\n" );
document.write( "Main Pyramid:			Smaller Pyramid:<BR>\n" );
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document.write( "Base length: …				base length: …<BR>\n" );
document.write( "Height: …				height: …<BR>\n" );
document.write( "Volume: …				volume : …<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 #569839 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Firstly let us write the data given \r<BR>\n" );
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document.write( "Tallest pyramid<BR>\n" );
document.write( "height = h<BR>\n" );
document.write( "base = b<BR>\n" );
document.write( "h/b = 2/3\r<BR>\n" );
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document.write( "b=(3/2) h\r<BR>\n" );
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document.write( "Volume of this pyramid= 1/3 * (3/2*h)^2*h<BR>\n" );
document.write( "=1/3 * 9/4h^3<BR>\n" );
document.write( "=(3/4)h^3\r<BR>\n" );
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document.write( "Volume of smaller pyramid\r<BR>\n" );
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document.write( "height = h/2<BR>\n" );
document.write( "(h/2)/b = 2/3\r<BR>\n" );
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document.write( "b= (3h/4)\r<BR>\n" );
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document.write( "V= 1/3 * (3h/4)^2*(h/2)\r<BR>\n" );
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document.write( "=1/3 * 9h^2/16 *h/2\r<BR>\n" );
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document.write( "=3h^3/32\r<BR>\n" );
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document.write( "Vol of 3 pyramids = 3*3h^3/32= 9h^3/32\r<BR>\n" );
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document.write( "Sum of volumes = 30 million cu.ft\r<BR>\n" );
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document.write( "(3h^3/4) +(3h^3/32)= 3*10^7 cu.ft<BR>\n" );
document.write( "multiply equation by 32\r<BR>\n" );
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document.write( "24h^3+3h^3= 32*3*10^7\r<BR>\n" );
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document.write( "27h^3= 96*10^7<BR>\n" );
document.write( "h^3= 96/27 *10^7<BR>\n" );
document.write( "h=328.82<BR>\n" );
document.write( "base = 1.5*328.82=493.24 feet\r<BR>\n" );
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document.write( "Smaller pyramid<BR>\n" );
document.write( "height = h/2 = 328.82/2=164.4 feet<BR>\n" );
document.write( "base = 1.5 * 164.4=246.6 feet\r<BR>\n" );
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document.write( "apply formula and find individual volmes\r<BR>\n" );
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