- #1
jaruta
- 2
- 0
Hello,
My problem regards the disk|washer, and cylindrical shell methods for finding volumes in single variable calc. My problem is basically am I understanding these two methods and their relationships properly.
Fundamentally, these methods are indentical, as we can arrive at the same solution whichever one we use. the difference is in the mechanics. At least that`s what I can tell from experience. The way in which I comprehend these methods is basically such that the washer method (which is essentially a corrolary to the disk method, no?) is applicable when the structure of the solid is such that one can infer the cross-sectional area; whereas, in the cyclidrical shell method one cannot. Moreover, because the rotation in the cylidrical shell method is parallel to the axis of revolution one would need to compute the max and min values and shift the solid to properly compute the volume once the area is revolved. Under this scenario, would it also be required to compute the thickness of the inner cylinder if it changed?
Homework Statement
My problem regards the disk|washer, and cylindrical shell methods for finding volumes in single variable calc. My problem is basically am I understanding these two methods and their relationships properly.
Fundamentally, these methods are indentical, as we can arrive at the same solution whichever one we use. the difference is in the mechanics. At least that`s what I can tell from experience. The way in which I comprehend these methods is basically such that the washer method (which is essentially a corrolary to the disk method, no?) is applicable when the structure of the solid is such that one can infer the cross-sectional area; whereas, in the cyclidrical shell method one cannot. Moreover, because the rotation in the cylidrical shell method is parallel to the axis of revolution one would need to compute the max and min values and shift the solid to properly compute the volume once the area is revolved. Under this scenario, would it also be required to compute the thickness of the inner cylinder if it changed?