{"id":1170,"date":"2021-06-30T17:02:03","date_gmt":"2021-06-30T17:02:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/introduction-to-volumes-of-revolution-cylindrical-shells\/"},"modified":"2021-11-17T02:02:44","modified_gmt":"2021-11-17T02:02:44","slug":"introduction-to-volumes-of-revolution-cylindrical-shells","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/introduction-to-volumes-of-revolution-cylindrical-shells\/","title":{"raw":"Introduction to Volumes of Revolution: Cylindrical Shells","rendered":"Introduction to Volumes of Revolution: Cylindrical Shells"},"content":{"raw":"

What you\u2019ll learn to do:\u00a0Compare different integration methods for determining volume<\/h2>\r\nIn this section, we examine the method of cylindrical shells, the final method for finding the volume of a solid of revolution. We can use this method on the same kinds of solids as the disk method or the washer method; however, with the disk and washer methods, we integrate along the coordinate axis parallel to the axis of revolution. With the method of cylindrical shells, we integrate along the coordinate axis perpendicular<\/em> to the axis of revolution. The ability to choose which variable of integration we want to use can be a significant advantage with more complicated functions. Also, the specific geometry of the solid sometimes makes the method of using cylindrical shells more appealing than using the washer method. In the last part of this section, we review all the methods for finding volume that we have studied and lay out some guidelines to help you determine which method to use in a given situation.","rendered":"

What you\u2019ll learn to do:\u00a0Compare different integration methods for determining volume<\/h2>\n

In this section, we examine the method of cylindrical shells, the final method for finding the volume of a solid of revolution. We can use this method on the same kinds of solids as the disk method or the washer method; however, with the disk and washer methods, we integrate along the coordinate axis parallel to the axis of revolution. With the method of cylindrical shells, we integrate along the coordinate axis perpendicular<\/em> to the axis of revolution. The ability to choose which variable of integration we want to use can be a significant advantage with more complicated functions. Also, the specific geometry of the solid sometimes makes the method of using cylindrical shells more appealing than using the washer method. In the last part of this section, we review all the methods for finding volume that we have studied and lay out some guidelines to help you determine which method to use in a given situation.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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