Volume by disks, shells, or washers?

[KMcFadden]

What is the easiest way to determine if the volume of a solid should be found by using disks, shells, or washers?

 

[encorelui2]

Personally I always start with the shell method unless it is a really basic, simple shape(disk method)... But to answer ur question, I look for a hole. If there is one, then i am thinking washer, if there isn't and the solid is a very simple shape, then I go with the disk method. For the most complex shapes, i automatically go to the shell method.

 

[Mark44]

What is the easiest way to determine if the volume of a solid should be found by using disks, shells, or washers?

There is no one-size-fits-all guidance here. It depends on the function/functions that bound the region being revolved. The disk and washer methods are essentially the same, with the washer method being used if the typical volume element is a disk with a hole in it.

Sometimes one method produces an integral that's easier to evaluate, and sometimes another method does.