Volume Slicing: Identifying Annulous Solids of Revolution

[kr73114]

Most of the time I can visualise whether some solids of revolution are annulous or not but sometimes I just don't see it. Can anyone tell me if I am missing something? Is there any way of knowing if the cross section is annulous? Please help...

 

[tiny-tim]

hi kr73114!

i don't get it …

by definition of a solid of revolution, doesn't the boundary of any slice have to be a circle? …

if there's only one circle, the slice is a disc, if there's two, it's an annulus, if there's three it's an annulus round a disc, and so on

 

[kr73114]

yeh...but how do you know if there are two circles?

 

[tiny-tim]

where do the circles come from?

 

[kr73114]

where do the circles come from?

i was hoping you could tell me?