document.write( "Question 50803: 1. Rubber bungs are made by removing the tops of cones. Starting with a cone of radius 10cm and height 16cm, a rubber bungs made by cutting a cone of radius 5 cm and height 8cm from the top. Find the volume and total surface area of the rubber bung.\r
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Algebra.Com's Answer #33830 by AnlytcPhil(1806)\"\" \"About 
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1. Rubber bungs are made by removing the tops of cones. Starting\r\n" );
document.write( "with a cone of radius 10cm and height 16cm, a rubber bungs made \r\n" );
document.write( "by cutting a cone of radius 5 cm and height 8cm from the top. \r\n" );
document.write( "Find the volume and total surface area of the rubber bung.\r\n" );
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document.write( "They start with a rubber cone whose cross section is like this:\r\n" );
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document.write( "             /|\\r\n" );
document.write( "            / | \\r\n" );
document.write( "         S /  |  \\r\n" );
document.write( "          /   |16 \\r\n" );
document.write( "         /    |    \\r\n" );
document.write( "        /_____|_____\\r\n" );
document.write( "           10\r\n" );
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document.write( "This has a volume of pr³/3 = p(10)³/3 = 1000p/3\r\n" );
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document.write( "Its surface area is found by\r\n" );
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document.write( "Lateral Surface Area = prS, where S = slant height\r\n" );
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document.write( "(Note: Lateral Surface Area does not include the circular base)\r\n" );
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document.write( "Lateral Surface Area = prS = p(10)S = 10pS \r\n" );
document.write( "     _______    ___________    _______    ___    _____     __ \r\n" );
document.write( "S = Ör² + h² = Ö(10)²+(15)² = Ö100+225 = Ö325 = Ö25·13 = 5Ö13 \r\n" );
document.write( "                                   __        __\r\n" );
document.write( "Lateral Surface Area = prS = 10p(5Ö13) = 50pÖ13\r\n" );
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document.write( "Base (circle) Surface Area = pr² = p(10)² = 100p\r\n" );
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document.write( "Total Surface Area = Lateral surface area + Base surface area  \r\n" );
document.write( "                         __               __\r\n" );
document.write( "Total Surface Area = 50pÖ13 + 100p = 50p(Ö13 + 2)\r\n" );
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document.write( "Then they cut away a rubber cone whose cross section is like this:\r\n" );
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document.write( "             /|\\r\n" );
document.write( "          S / |8\\r\n" );
document.write( "           /__|__\\r\n" );
document.write( "            5\r\n" );
document.write( "This has a volume of pr³/3 = p(5)³/3 = 125p/3\r\n" );
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document.write( "Its surface area is found by\r\n" );
document.write( "                          \r\n" );
document.write( "Lateral Surface Area = prS, where S = slant height\r\n" );
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document.write( "Lateral Surface Area = prS = p(5)S = 5pS \r\n" );
document.write( "     _______    _________    _____    __    \r\n" );
document.write( "S = Ör² + h² = Ö(5)²+(8)² = Ö25+64 = Ö89  \r\n" );
document.write( "                                 __       __\r\n" );
document.write( "Lateral Surface Area = prS = 5p(Ö89) = 5pÖ89\r\n" );
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document.write( "Note: They cut away only the lateral surface area of this small cone.\r\n" );
document.write( "(Its base circle must then be added to find the total surface \r\n" );
document.write( "area of the bung)   \r\n" );
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document.write( "-----------------------------------------\r\n" );
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document.write( "They end up with a rubber bung whose cross section is like this:\r\n" );
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document.write( "           _5_____\r\n" );
document.write( "          /   |   \\r\n" );
document.write( "         /    |    \\r\n" );
document.write( "        /_____|_____\\r\n" );
document.write( "          10\r\n" );
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document.write( "Volume of bung = Volume of large cone - Volume of small cone  \r\n" );
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document.write( "Volume of bung = 1000p/3 - 125p/3 = 875p/3\r\n" );
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document.write( "That's approximately 916.3 cubic centimeters.\r\n" );
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document.write( "Total Surface Area of bung =\r\n" );
document.write( "   Total Surface Area of large Cone - \r\n" );
document.write( "        Lateral Surface Area only of small Cone +\r\n" );
document.write( "             Area of base of small cone (circular top of bung)\r\n" );
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document.write( "Area of circular top of bung = pr² = p(5)² = 25p\r\n" );
document.write( "                                  __           __\r\n" );
document.write( "Total Surface Area of bung = 50p(Ö13 + 2) - 5pÖ89 + 25p \r\n" );
document.write( "                                    __         __             \r\n" );
document.write( "Total Surface Area of bung = 5p[10(Ö13 + 2) - Ö89 + 5]\r\n" );
document.write( "                                   __         __             \r\n" );
document.write( "Total Surface Area of bung = 5p[10Ö13 + 20 - Ö89 + 5]\r\n" );
document.write( "                                   __    __             \r\n" );
document.write( "Total Surface Area of bung = 5p(10Ö13 - Ö89 + 25)\r\n" );
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document.write( "That's approximately 810.9 square centimeters.\r\n" );
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document.write( "Edwin
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