document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818790>Question 818790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A vitamin tablet is 2.4 cm long and is in the shape of a cylinder with hemispheres of diameter 0.6 cm attached to both ends. Another vitamin tablet is in the shape of a cylinder of height 0.6 cm. Find:<BR>\n" );
document.write( "a) The radius of the cylindrical tablet given that it's surface area is equal to that of the first tablet, and,<BR>\n" );
document.write( "b) The volume of each tablet. <BR>\n" );
document.write( "Ans a) 0.6<BR>\n" );
document.write( "b)0.622 cm(cube), 0.679 cm(cube) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492816 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=492816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 2.4 cm long tablet has an overall length of 2.4 cm (including those two hemispheres at both ends).<BR>\n" );
document.write( "It has two hemisphere end caps with radius 0.3 cm attached to the bases of a cylinder with a height of<BR>\n" );
document.write( "2.4 cm - 0.3 cm - 0.3 cm = 1.8 cm.<BR>\n" );
document.write( "Its surface area is the lateral area of the cylindrical part,<BR>\n" );
document.write( "plus the area of the two hemispheres (the area of one sphere).<BR>\n" );
document.write( "Its volume is the volume of the cylindrical part,<BR>\n" );
document.write( "plus the volume of the two hemispheres (the volume of one sphere).<BR>\n" );
document.write( " <BR>\n" );
document.write( "Formulas:<BR>\n" );
document.write( "area of a sphere = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"4pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "volume of a sphere = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"4pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "lateral area of a cylinder = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar%2Ah ALIGN=MIDDLE  ALT=\"2pi%2Ar%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "total area of a cylinder = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar%5E2%2B2pi%2Ar%2Ah ALIGN=MIDDLE  ALT=\"2pi%2Ar%5E2%2B2pi%2Ar%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "volume of a cylinder = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >= radius and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >= height,<BR>\n" );
document.write( "which we will measure in cm.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Surface area of the 2.4 cm long tablet (in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2A0.3%2A1.8%2B4pi%2A0.3%5E2=1.08pi%2B0.36pi=1.44pi ALIGN=MIDDLE  ALT=\"2pi%2A0.3%2A1.8%2B4pi%2A0.3%5E2=1.08pi%2B0.36pi=1.44pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Surface area of the cylindrical tablet (in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar%5E2%2B2pi%2Ar%2A0.6=2pi%2Ar%5E2%2B1.2pi ALIGN=MIDDLE  ALT=\"2pi%2Ar%5E2%2B2pi%2Ar%2A0.6=2pi%2Ar%5E2%2B1.2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the surface areas are the same,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar%5E2%2B1.2pi=1.44pi ALIGN=MIDDLE  ALT=\"2pi%2Ar%5E2%2B1.2pi=1.44pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dividing both sides of the equal sign by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%5E2%2B1.2=1.44 ALIGN=MIDDLE  ALT=\"2r%5E2%2B1.2=1.44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dividing both sides of the equal sign by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2B0.6=0.72 ALIGN=MIDDLE  ALT=\"r%5E2%2B0.6=0.72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving by completing the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2B0.6%2B0.09=0.72%2B0.09 ALIGN=MIDDLE  ALT=\"r%5E2%2B0.6%2B0.09=0.72%2B0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B0.3%29%5E2=0.81 ALIGN=MIDDLE  ALT=\"%28r%2B0.3%29%5E2=0.81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B0.3=sqrt%280.81%29 ALIGN=MIDDLE  ALT=\"r%2B0.3=sqrt%280.81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only useful (positive) solution.<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B0.3=0.9 ALIGN=MIDDLE  ALT=\"r%2B0.3=0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.9-0.3 ALIGN=MIDDLE  ALT=\"r=0.9-0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=0.6cm%29 ALIGN=MIDDLE  ALT=\"highlight%28r=0.6cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Volume of the 2.4 cm long tablet (in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E3 ALIGN=MIDDLE  ALT=\"cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A0.3%5E2%2A1.8%2B4pi%2A0.3%5E3%2F3=0.162pi%2B0.036pi=1.98pi ALIGN=MIDDLE  ALT=\"pi%2A0.3%5E2%2A1.8%2B4pi%2A0.3%5E3%2F3=0.162pi%2B0.036pi=1.98pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=+about%22 ALIGN=MIDDLE  ALT=\"%22=+about%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.622cm%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%280.622cm%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Volume of the cylindrical tablet (in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E3 ALIGN=MIDDLE  ALT=\"cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A0.6%5E2%2A0.6=0.216pi ALIGN=MIDDLE  ALT=\"pi%2A0.6%5E2%2A0.6=0.216pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=+about%22 ALIGN=MIDDLE  ALT=\"%22=+about%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.679cm%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%280.679cm%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );