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Math 122 Fall 2008 Unit Test 2 Review Problems Set A We have chosen these problems because we think that they are representative of many of the mathematical concepts that we have studied There is no guarantee that the problems that appear on the exam will resemble these problems in any way whatsoever Remember that on exams you will have to supply evidence for your conclusions and may have to explain why your answers are reasonable and appropriate 1 Corks for wine bottles are usually from strips of bark from the cork tree Phellodendron amurense A cork from a typical bottle is a roughly cylindrical shape whose volume can be determined with the formula V r2 h where r is the radius of the cork and h is the height of the cork Simple cylindrical corks are most suitable for still wines That is wines that do not have any carbonation due to dissolved CO2 present in the wine Corks for sparkling wines the best known being the wines from the Champagne region of France are designed quite differently see photograph1 This is because the contents of a bottle of sparkling wine are under very high pressure often five times regular atmospheric pressure or higher The cork for a bottle of sparkling wine has to both seal the bottle the function of any cork and to resist the strong forces exerted on it by the pressurized contents of the wine bottle In this problem you will calculate the volume of a champagne cork and the volume of a conventional cork for the sake of comparison a A conventional cork from a bottle of still wine typically measures about 4 4cm in length with a radius of about 0 9 cm Calculate the volume of a conventional cork in cubic centimeters Figure 6 Cork for a bottle of Champagne b Figure 7 shows a shaded area which when revolved around the xaxis creates a reasonable approximation for the shape of a cork from a bottle of Perrier Jouet Brut Imperial Champagne vintage 1994 Sketch a three dimensional picture of the shape that will be formed by revolving the shaded area

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