ch6sc2notes - Math 104 Rimmer 6.2 Volumes by Cylindrical Shells 6.2 Volumes by Cylindrical Shells Sometimes finding the volume of a solid of revolution

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1/23/2012 1 Math 104 – Rimmer 6.2 Volumes by Cylindrical Shells Sometimes finding the volume of a solid of revolution is impossible by the disk or washer method ( ) 2 sin y x = π Since there is a gap b/w the region and the axis of rotation, we would try washer method We would have to solve for as a function of since the axis of rotation is vertical. Sometimes this is the problem, but we can do it here. x y 1 sin x y - = Our problem is that the outer radius and the inner radius use the . same curve In order to find the volume of this solid of revolution we need a different technique. 6.2 Volumes by Cylindrical Shells Math 104 – Rimmer 6.2 Volumes by Cylindrical Shells The Method of Cylindrical Shells uses the volume of nested cylinders to find the volume of a solid of revolution. To understand the formula, lets first look at one of the cylindrical shells: There are two cylinders, an outer cylinder and an inner cylinder.