document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=367095>Question 367095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylindrical hot water tank has an outside diameter of 0.4 yards and a height of 1.2 yards. It's outside is to be completely covered with an insulating material which is 1.2 inches thick. Calculate the volume of the insulating material required.<BR>\n" );
document.write( "I found lateral surface area of 1.507964474. area of bottom of 0.125663706 for a total area of 1.63362818. Do I need to compensate for the top too? Where do I go next to get the volume of material? Thank you in advance for any help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #261742 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=261742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you do not need lateral area to solve this.\r<BR>\n" );
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document.write( "you need volume only.\r<BR>\n" );
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document.write( "the basic idea is to take the volume of the cylinder with the insulation and subtract from that the volume of the cylinder without the insulation.\r<BR>\n" );
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document.write( "the difference is the volume of the insulation.\r<BR>\n" );
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document.write( "the tank has an outside diameter of .4 yards and a height of 1.2 yards.\r<BR>\n" );
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document.write( "the thickness of the insulation material is 1.2 inches.\r<BR>\n" );
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document.write( "this increases the diameter of the cylinder by 2.4 inches (1.2 inches on each opposite side).\r<BR>\n" );
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document.write( "this also increases the height of the cylinder by 2.4 inches (1.2 inches on each top or bottom).\r<BR>\n" );
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document.write( "2.4 inches is equivalent to 2.4 / 12 / 3 = .0666666667 yards.\r<BR>\n" );
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document.write( "you need to add this to the diameter of the cylinder and to the height of the cylinder.\r<BR>\n" );
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document.write( "the diameter of the cylinder increases to .46666666667 yards with the width of the insulation added.\r<BR>\n" );
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document.write( "the height of the cylinder increases to 1.2666666667 yards with the width of the insulation added./\r<BR>\n" );
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document.write( "the formula for volume of a cylinder is equal to pi * r^2 * h.\r<BR>\n" );
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document.write( "r is the radius and h is the height.\r<BR>\n" );
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document.write( "the radius of the cylinder is equal to 1/2 the diameter.\r<BR>\n" );
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document.write( "1/2 the diameter of .4 yards is equal to .2 yards.\r<BR>\n" );
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document.write( "1/2 the diameter of .46666666667 yards is equal to .2333333333 yards.\r<BR>\n" );
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document.write( "the volume of the cylinder without the insulation is equal to pi * .2^2 * 1.2 which equals .048 * pi.\r<BR>\n" );
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document.write( "the volume of the cylinder with the insulation is equal to pi * .233333333^2 * 1.2666666667 yards which equals .068962963 * pi.\r<BR>\n" );
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document.write( "the volume of the insulation is equal to the volume of the cylinder with the insulation minus the volume of the cylinder without the insulation.\r<BR>\n" );
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document.write( "the volume of the insulation is therefore equal to .068962963 minus .048 which equals .020962963 * pi cubic yards.\r<BR>\n" );
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document.write( "multiply this by pi to get .065857091 cubic yards.\r<BR>\n" );
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document.write( "multiply this by 36^3 to get 3072.628417 cubic inches.\r<BR>\n" );
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document.write( "if you wanted to solve this by inches to start with, you would have done the following:\r<BR>\n" );
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document.write( "height of the tank without insulation is 1.2 yards * 3 * 12 = 43.2 inches.\r<BR>\n" );
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document.write( "diameter of the tank without insulation is .4 yards * 3 * 12 = 14.4 inches.\r<BR>\n" );
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document.write( "the height of the tank with insulation is 43.2 inches + (2*1.2) inches which equals a total of 45.6 inches.\r<BR>\n" );
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document.write( "the diameter of the tank with insulation is 14.4 inches + (2*1.2) inches which equals a total of 16.8 inches.\r<BR>\n" );
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document.write( "the radius of the tank is equal to 1/2 the diameter of the tank.\r<BR>\n" );
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document.write( "the radius of the tank without insulation is equal to 14.4 / 2 = 7.2 inches.\r<BR>\n" );
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document.write( "the radius of the tank with insulation is equal to 16.8 / 2 = 8.4 inches.\r<BR>\n" );
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document.write( "the volume of the tank without the insulation is equal to pi * 7.2^2 * 43.2 which equals pi * 2239.488 cubic inches.\r<BR>\n" );
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document.write( "the volume of the tank with the insulation is equal to pi * 8.4^2 * 45.6 which equals pi * 3217.536 cubic inches.\r<BR>\n" );
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document.write( "the volume of the insulation is the volume of the tank with the insulation minus the volume of the tank without the insulation.\r<BR>\n" );
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document.write( "this equals pi * 2239.488 cubic inches subtracted from pi * 3217.536 cubic inches which equals pi * 978.048 cubic inches.\r<BR>\n" );
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document.write( "if you multiply this by pi, you get an answe4r of 3072.628412 cubic inches.\r<BR>\n" );
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document.write( "if you divide this by 36^2, you get an answer of .06585709 cubic yards.\r<BR>\n" );
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document.write( "the answer you get if you convert everything to yards is the same answer that you get if you convert everything to inches.\r<BR>\n" );
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document.write( "it's just a matter of preference which way you want to go.\r<BR>\n" );
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