Advice on volume of solids NOT of revolution?

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Homework Help Overview

The discussion revolves around finding volumes of solids that are not solids of revolution, highlighting the challenges faced by participants when approaching these types of problems compared to those involving revolving solids.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants express a need for general strategies to tackle volume calculations for non-revolution solids and inquire about the nature of typical cross sections. Questions arise regarding how cross sections vary based on the specific solid in question.

Discussion Status

Some participants have offered suggestions, such as researching Cavalieri solids and discussing the characteristics of cross sections for different shapes. However, there is no explicit consensus on a singular approach, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants note the difficulty in starting these problems and the lack of a general method for arbitrary three-dimensional solids, indicating a need for further clarification and examples.

Gauss177
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Anyone have any advice for finding volumes of solids that are not solids of revolution? I have a much more difficult time starting these kinds of problems compared to revolving ones.
 
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Gauss177 said:
Anyone have any advice for finding volumes of solids that are not solids of revolution? I have a much more difficult time starting these kinds of problems compared to revolving ones.

I'm not sure anyone can help you unless you become a bit more specific.
 
I mean general things to do or whatever to start these kinds of problems. And also what would a typical cross section be like? Whereas when using washer method/shell method the solid is revolved so cross sections are circular, do the cross sections for these problems depend entirely on the question?

for example:
A hole of radius r is bored through a cylinder of radius R > r at right angles to the axis of the cylinder. Set up an integral (no need to evaluate) for the volume cut out.
 
If you know the function which defines the cross section, then you can calculate the integral. You may want to do some google-ing on Cavalieri solids. I hope I was at least a bit helpful. :wink:
 
say you are integrating a cube, then the area of a typical cross section would be l*w. for a cone it is pi*r^2 etc..it really depends on what kind of solids you are trying to find the volume of. But a cross section is just an infinitely thin slice out of the solid.
 
There is no general method for finding the volume of an arbitrary 3 dimensional solid.
 
Yes there is, putting it in water :D
 

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