document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287598>Question 287598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right circular cylinder is given. If the radius is increased by 25% then the volume will stay the same if the height is increased/decreased by what percent?\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Increased by 64% (b) Decreased by 36% (c) Decreased by 25% <BR>\n" );
document.write( "(d) Increased by 25% (e) None of the above </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208366 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=208366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A right circular cylinder is given. If the radius is increased by 25% then the volume will stay the same if the height is increased/decreased by what percent? <BR>\n" );
document.write( "(a) Increased by 64% (b) Decreased by 36% (c) Decreased by 25% <BR>\n" );
document.write( "(d) Increased by 25% (e) None of the above\r<BR>\n" );
document.write( "\n" );
document.write( "Let r be the original radius, h the original height and H the new increased height.  Then we have:\r<BR>\n" );
document.write( "\n" );
document.write( "1.) volume of original cylinder = pi*(r^2)*h<BR>\n" );
document.write( "2.) volume of cylinder with increased radius = pi*(1.25r)^2*H\r<BR>\n" );
document.write( "\n" );
document.write( "For the volume not to change we must have:\r<BR>\n" );
document.write( "\n" );
document.write( "pi*(r^2)*h = pi*(5/4*r)^2*H<BR>\n" );
document.write( "pi*(r^2)*h = pi*25/16*r^2*H\r<BR>\n" );
document.write( "\n" );
document.write( "Divide both sides above by pi:\r<BR>\n" );
document.write( "\n" );
document.write( "r^2*h = (25/16)*r^2*H\r<BR>\n" );
document.write( "\n" );
document.write( "Divide both sides by r^2:\r<BR>\n" );
document.write( "\n" );
document.write( "h = (25/16)*H<BR>\n" );
document.write( "H = (16/25)*h<BR>\n" );
document.write( "H = .64*h\r<BR>\n" );
document.write( "\n" );
document.write( "The height must be DECREASED by .36, that is 36%.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );