Volume Slicing: Identifying Annulous Solids of Revolution

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around identifying annulous solids of revolution, particularly focusing on how to determine if a cross section of such solids contains one or more circles. Participants explore the definitions and visualizations associated with these geometric shapes.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses difficulty in visualizing whether certain solids of revolution are annulous and seeks guidance on identifying these shapes.
  • Another participant suggests that by definition, the boundary of any slice of a solid of revolution must be a circle, proposing that the number of circles determines the type of cross section.
  • There is a question about how to ascertain the presence of two circles in a cross section, indicating uncertainty in the identification process.
  • Further inquiry is made regarding the origin of the circles in the context of solids of revolution, suggesting a need for clarification on this aspect.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are multiple questions and uncertainties regarding the identification of circles in solids of revolution and the criteria for determining annulous shapes.

Contextual Notes

The discussion highlights a lack of clarity on the definitions and visualizations of solids of revolution, particularly concerning the identification of cross sections with multiple circles. There are unresolved questions about the criteria for determining whether a cross section is annulous.

kr73114
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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...
 
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hi kr73114! :smile:

i don't get it :confused: …

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 :wink:
 
yeh...but how do you know if there are two circles?
 
where do the circles come from? :wink:
 
tiny-tim said:
where do the circles come from? :wink:

i was hoping you could tell me?
 

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