document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83754>Question 83754</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977274/algebrahomeworkh>Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A regular square pyramid is inscribed in a come with radius 4 cm. and height 4 cm.\r<BR>\n" );
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document.write( "A. What is the volume of the pyramid?<BR>\n" );
document.write( "   I know that the volume of the pyramid equals Lateral Area+Base, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5pl ALIGN=MIDDLE  ALT=\".5pl\"   DISABLED_style= \"max-width:90%; height:auto;\" > P being the perimeter of the base and L being the slant height. I am not able to get beyond this point on matter how hard I try. <BR>\n" );
document.write( "B. Find the slant height of the pyramid and the cone.<BR>\n" );
document.write( "   I have tried at this one many times but have not been able to get anything. I know that the slant height forms a triangle with the radius and the height, but I do not know where to go from there.\r<BR>\n" );
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document.write( "Please 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 #60244 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=60244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A regular square pyramid is inscribed in a come with radius 4 cm. and height 4 cm. <BR>\n" );
document.write( "Draw the figure of the reg sq pyramid in the cone; draw the diameter = 8 cm<BR>\n" );
document.write( "of the base of the cone; draw the altitude = 4 cm of the pyramid = the altitude<BR>\n" );
document.write( "of the cone.<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "A. What is the volume of the pyramid?<BR>\n" );
document.write( "V = (1/3)(area of base)(altitude)<BR>\n" );
document.write( "The diagonal of the base is the diameter of the cone = 8 cm<BR>\n" );
document.write( "Radius of the base = 4 cm<BR>\n" );
document.write( "Side of the square base = 4/sqrt2<BR>\n" );
document.write( "Therefore Area of the base = (side)^2 = (4/sqrt2)^2 = 16/2 = 8 sq cm<BR>\n" );
document.write( "So, Volume = (1/3)(8)(4) = 32/3 cu cm.<BR>\n" );
document.write( "=========================================<BR>\n" );
document.write( "I know that the volume of the pyramid equals Lateral Area+Base, which is  P being the perimeter of the base and L being the slant height. I am not able to get beyond this point on matter how hard I try. <BR>\n" );
document.write( "B. Find the slant height of the pyramid and the cone.<BR>\n" );
document.write( "Draw the slant height of the pyramid.<BR>\n" );
document.write( "It is the hypotenuse of a rt. triangle with sides 4 and (1/2)(4/sqrt2)<BR>\n" );
document.write( "or 4 and 2sqrt2.<BR>\n" );
document.write( "hyp^2=(2sqrt2)^2+4^2 = = 8 + 16 = 24<BR>\n" );
document.write( "hyp = 2sqrt6<BR>\n" );
document.write( "So, slant height of the pyramid = 2sqrt6 cm<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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