document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101549>Question 1101549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a woodworker makes different sizes of wooden blocks in the shape of cones. the narrowest block the worker makes a radius r=8 centimeters and a height h=22 centimeters. For each centimeter increase in the radius the worker decreases the height of the cone four centimeters. Write a function V(x) to represent the volume of each cone the worker makes as a function of x. What are the roots of the equation? What is the domain that makes sense for this problem? Explain your reasoning. Calculate the volume for each integer value x in this domain. For what integer value of x is the volume of the cone a maximum? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716242 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a woodworker makes different sizes of wooden blocks in the shape of cones.<BR>\n" );
document.write( " the narrowest block the worker makes a radius r=8 centimeters and a height h=22 centimeters.<BR>\n" );
document.write( " For each centimeter increase in the radius the worker decreases the height of the cone four centimeters.<BR>\n" );
document.write( " Write a function V(x) to represent the volume of each cone the worker makes as a function of x.<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah%29 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is volume of a cone<BR>\n" );
document.write( "let x = no. of cm increases and no. of 4cm decreases<BR>\n" );
document.write( "V(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%288%2Bx%29%5E2+%2A+%2822-4x%29 ALIGN=MIDDLE  ALT=\"pi%2A%288%2Bx%29%5E2+%2A+%2822-4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " What are the roots of the equation?<BR>\n" );
document.write( "x = -8<BR>\n" );
document.write( "and<BR>\n" );
document.write( "-4x = -22<BR>\n" );
document.write( "x = +5.5<BR>\n" );
document.write( " What is the domain that makes sense for this problem?<BR>\n" );
document.write( "x=0 to x=5<BR>\n" );
document.write( "When x > 5 the height becomes a neg number<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Calculate the volume for each integer value x in this domain.<BR>\n" );
document.write( " x | V(x)<BR>\n" );
document.write( "----------<BR>\n" );
document.write( " 0 | 1474.5<BR>\n" );
document.write( " 1 | 1526.8 Max volume<BR>\n" );
document.write( " 2 | 1466.1<BR>\n" );
document.write( " 3 | 1267.1<BR>\n" );
document.write( " 4 | 904.8<BR>\n" );
document.write( " 5 | 353.9<BR>\n" );
document.write( ":<BR>\n" );
document.write( " For what integer value of x is the volume of the cone a maximum? x = 1   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );