Cylindrical shell and cross-section volume concept question

[kylera]

When a problem with a number of equations is given, asking to find its volume, a student has a choice between the cylindrical shell method and the cross-section method. However, regardless of what method is chosen, do both answers end up being EXACTLY the same?

 

[Defennder]

Yes. The "cross-section method" is also known as the washer method. It depends on whether you want to re-express x in terms of y or the reverse to get the volume by either method.