document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=880998>Question 880998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question makes me crazy , please help me dear tutor . Find the height of a cylinder of maximum volume which can be cut from a cone of height 15cm and base radius 7.5cm . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #531859 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=531859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A linear relationship is between the cone's height above its base and the distance from center of the base.  This slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F%287.5%29 ALIGN=MIDDLE  ALT=\"17%2F%287.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34%2F15 ALIGN=MIDDLE  ALT=\"34%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You can view this slope as negative and form an equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%2834%2F15%29x%2B17 ALIGN=MIDDLE  ALT=\"y=-%2834%2F15%29x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "What is the formula for VOLUME of the cylinder cut from this cone?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=pi%2Ax%5E2%2Ay ALIGN=MIDDLE  ALT=\"v=pi%2Ax%5E2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x is the radius, y is the height.  Having our formula, linear equation, for y means we can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=pi%2Ax%5E2%2A%28-%2834%2F15%29x%2B17%29 ALIGN=MIDDLE  ALT=\"v=pi%2Ax%5E2%2A%28-%2834%2F15%29x%2B17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=pi%2Ax%5E2%2817-%2834%2F15%29x%29 ALIGN=MIDDLE  ALT=\"v=pi%2Ax%5E2%2817-%2834%2F15%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=pi%2A17x%5E2-pi%2834%2F15%29x%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%28v=pi%2A17x%5E2-pi%2834%2F15%29x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "An obvious restriction is to use only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C7.5 ALIGN=MIDDLE  ALT=\"0%3Cx%3C7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This appears to be a derivative and function maximization exercise, but I'm stopping my part of the solution here.  You could also use a graphing calculator to look for the maximum value for v.\r<BR>\n" );
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document.write( "(Using Calculus, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx ALIGN=MIDDLE  ALT=\"dv%2Fdx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and equate to zero, solve for x.  Compute v that corresponds)\r<BR>\n" );
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document.write( "(Further note -  Actually, once you find x, you want to go to the formula for y to find the height where to cut the cone.) </SPAN>\n" );
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