ch6sc2 - Math 104 Rimmer 6.2 Volumes by Cylindrical Shells 6.2 Volumes by Cylindrical Shells Sometimes finding the volume of a solid of revolution

# ch6sc2 - Math 104 Rimmer 6.2 Volumes by Cylindrical...

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1Math 104 – Rimmer6.2 Volumes by Cylindrical ShellsSometimes finding the volume of a solid of revolution isimpossibleby the disk or washer method2sinyxSince there is a gap b/w the region and the axis of rotation, we would try washer methodWe 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.xy1sinxyOur problem is that the outer radius and the innerradius use the .same curveIn order to find the volume of this solid of revolution we need a different technique.6.2 Volumes by Cylindrical ShellsMath 104 – Rimmer6.2 Volumes by Cylindrical ShellsThe Method of Cylindrical Shellsuses the volume of nested cylindersto 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.The volume of the shellwe use is found by taking the volume of the inner cylinder and subtracting it from the volume of the outer cylinder.shellouterinnerVVVouterrinnerr22shellouterinnerVrhrh22shellouterinnerVhrrshellouterinnerouterinnerVhrrrr22outerinnershellouterinner