document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149716>Question 149716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The rate at which a tablet of vitamin C begins to dissolve depends on the surface area of the tablet. One brand of tablet is 2 centimeters long and is in the shape of a cylinder with hemispheres of diameter 0.5 centimeter attached to both ends. A second brand of tablet is to be manufactured in the shape of a right circular cylinder of altitude 0.5 centimeter.\r<BR>\n" );
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document.write( "a) Find the diameter of the second tablet so that its surface are is equal to that of the first tablet.\r<BR>\n" );
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document.write( "b) Find the volume of each tablet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109969 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=109969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  One brand of tablet is 2 centimeters long and is in the shape of a cylinder with hemispheres of diameter 0.5 centimeter attached to both ends.<BR>\n" );
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document.write( " A second brand of tablet is to be manufactured in the shape of a right circular cylinder of altitude 0.5 centimeter.<BR>\n" );
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document.write( "a) Find the diameter of the second tablet so that its surface are is equal to that of the first tablet.<BR>\n" );
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document.write( "Find the surface area of the 1st tablet<BR>\n" );
document.write( "The radius of the two hemispheres = .25<BR>\n" );
document.write( "The length of cylinder portion = 2 - .5 = 1.5 cm<BR>\n" );
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document.write( "S.A = (4*pi*.25^2) + (pi*.5*1.5)<BR>\n" );
document.write( "S.A = .7854 + 2.3562<BR>\n" );
document.write( "S.A = 3.1416 sq/cm of the 1st tablet<BR>\n" );
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document.write( "Find the radius of the 2nd tablet (h=.5) with the above S.A.<BR>\n" );
document.write( "2*pi*r^2 + 2*pi*r*.5 = 3.1416<BR>\n" );
document.write( "Divide both side by 2*pi<BR>\n" );
document.write( "r^2 + .5r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.1416%2F%282%2Api%29 ALIGN=MIDDLE  ALT=\"3.1416%2F%282%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r^2 + .5r = .5<BR>\n" );
document.write( "A quadratic equation:<BR>\n" );
document.write( "r^2 + .5r - .5 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(r+1)(r-.5) = 0<BR>\n" );
document.write( "Positive solution<BR>\n" );
document.write( "r = + .5 cm; diameter of the 2nd tablet = 1.0 cm<BR>\n" );
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document.write( "Check solution: pi*.5^2 + pi*1*.5 = 3.1416 sq/cm<BR>\n" );
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document.write( "b) Find the volume of each tablet.<BR>\n" );
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document.write( "Tablet 1; r=.25; h=1.5:<BR>\n" );
document.write( "V = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >*pi*.25^3) = (pi*.25^2*1.5)<BR>\n" );
document.write( "V = .06545 + .29452<BR>\n" );
document.write( "V = .360  cu/cm<BR>\n" );
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document.write( "Tablet 2; r=.5, h=.5:<BR>\n" );
document.write( "V = pi*.5^2*.5<BR>\n" );
document.write( "V = .3927 cu/cm   </SPAN>\n" );
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