document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622471>Question 622471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square prism in inscribed in a cylinder. The prism has a height of 12 inches and the cylinder has a radius of 5 inches. What's the lateral area and surface area of the prism and the cylinder </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391458 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=391458\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that from above you just see the bases of the prism and the cylinder, looking like a square inscribed in a circle, like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-6%2C6%2C-6%2C6%2C%0D%0Acircle%280%2C0%2C5%29%2C%0D%0Arectangle%28-3.535%2C-3.535%2C3.535%2C3.535%29%2C%0D%0Alocate%28-0.5%2C0.5%2C10%29%2C%0D%0Aarrow%280.5%2C0%2C5%2C0%29%2Carrow%28-0.5%2C0%2C-5%2C0%29%2C%0D%0Alocate%28-0.5%2C-2%2C5sqrt%282%29%29%2C%0D%0Aarrow%280.8%2C-2.5%2C3.535%2C-2.5%29%2Carrow%28-0.8%2C-2.5%2C-3.535%2C-2.5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The diameter of the circle is 10 inches, the length of the diagonal of the square.<BR>\n" );
document.write( "Two sides of the square, of length x inches, form a right triangle with the diagonal for a hypotenuse, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2=100 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=100 ALIGN=MIDDLE  ALT=\"2x%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=50 ALIGN=MIDDLE  ALT=\"x%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2850%29=sqrt%2825%2A2%29=sqrt%2825%29%2Asqrt%282%29=5sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2850%29=sqrt%2825%2A2%29=sqrt%2825%29%2Asqrt%282%29=5sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the circle (with radius 5) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A5%5E2=25pi ALIGN=MIDDLE  ALT=\"pi%2A5%5E2=25pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches.<BR>\n" );
document.write( "That circle is one of the two congruent (equal) bases of the cylinder.<BR>\n" );
document.write( "The circumference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A5=10pi ALIGN=MIDDLE  ALT=\"2%2Api%2A5=10pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches, and the lateral area of the cylinder is that times the height, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10pi%2A12=120pi ALIGN=MIDDLE  ALT=\"10pi%2A12=120pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches.<BR>\n" );
document.write( "So the total surface area of the cylinder is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120pi%2B2%2A25pi=170pi ALIGN=MIDDLE  ALT=\"120pi%2B2%2A25pi=170pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches.<BR>\n" );
document.write( "The area of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=50 ALIGN=MIDDLE  ALT=\"x%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches.<BR>\n" );
document.write( "That square is one of the two congruent (equal) bases of the prism.<BR>\n" );
document.write( "The perimeter of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A5sqrt%282%29=20sqrt%282%29 ALIGN=MIDDLE  ALT=\"4%2A5sqrt%282%29=20sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches, and the lateral area of the prism is that times the height, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20sqrt%282%29%2A12=120sqrt%282%29 ALIGN=MIDDLE  ALT=\"20sqrt%282%29%2A12=120sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches.<BR>\n" );
document.write( "So the total surface area of the cylinder is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120sqrt%282%29%2B2%2A50=120sqrt%282%29%2B100 ALIGN=MIDDLE  ALT=\"120sqrt%282%29%2B2%2A50=120sqrt%282%29%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches. </SPAN>\n" );
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