document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199778>Question 1199778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wooden right circular cylinder with diameter 9 cm and height 9 cm is topped with a hemisphere. The surface area, in cm^2, of the resulting shape is\r<BR>\n" );
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document.write( "a) 141.75π<BR>\n" );
document.write( "b) 182.25π<BR>\n" );
document.write( "c) 162π<BR>\n" );
document.write( "d) 405π<BR>\n" );
document.write( "e) 182.25 + 60.75π </SPAN>\n" );
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document.write( "A = surface area of the cylinder<BR>\n" );
document.write( "B = surface area of the hemisphere<BR>\n" );
document.write( "We'll use this to find A+B, but we'll do a bit of adjustment as I'll explain later.\r<BR>\n" );
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document.write( "r = radius = diameter/2 = 9/2 = 4.5 cm<BR>\n" );
document.write( "h = height = 9 cm\r<BR>\n" );
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document.write( "Cylinder:<BR>\n" );
document.write( "surface area of cylinder = 2pi*r^2 + 2pi*r*h<BR>\n" );
document.write( "surface area of cylinder = 2pi*r(r + h)<BR>\n" );
document.write( "A = 2pi*r(r + h)<BR>\n" );
document.write( "A = 2pi*4.5(4.5 + 9)<BR>\n" );
document.write( "A = 121.5pi\r<BR>\n" );
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document.write( "Hemisphere:<BR>\n" );
document.write( "surface area of hemisphere = (area of circular base)+(half of surface area of sphere)<BR>\n" );
document.write( "B = (pi*r^2) + (0.5*(4pi*r^2))<BR>\n" );
document.write( "B = pi*r^2 + 2pi*r^2<BR>\n" );
document.write( "B = 3pi*r^2<BR>\n" );
document.write( "B = 3pi*(4.5)^2<BR>\n" );
document.write( "B = 60.75pi\r<BR>\n" );
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document.write( "A+B = 121.5pi + 60.75pi<BR>\n" );
document.write( "A+B = 182.25pi\r<BR>\n" );
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document.write( "It appears choice (b) is the final answer. <BR>\n" );
document.write( "But be careful: this is trick/trap your teacher set up.\r<BR>\n" );
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document.write( "The calculation A+B counts the circular base of the hemisphere and the circular top of the cylinder.<BR>\n" );
document.write( "These two circles are NOT part of the external surface area. <BR>\n" );
document.write( "They are covered up when the shapes combine.<BR>\n" );
document.write( "Think of them as internal walls that are not part of the exterior of the house.\r<BR>\n" );
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document.write( "We'll subtract off two copies of pi*r^2 = pi*(4.5)^2 = 20.25pi<BR>\n" );
document.write( "So we subtract 2*20.25pi = 40.5pi square cm of area.\r<BR>\n" );
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document.write( "182.25pi - 40.5pi = 141.75pi\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>a)  141.75pi</font><BR>\n" );
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