Advice on volume of solids NOT of revolution?

[Gauss177]

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.

 

[radou]

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.

 

[Gauss177]

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.

 

[radou]

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.

 

[trajan22]

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.

 

[HallsofIvy]

There is no general method for finding the volume of an arbitrary 3 dimensional solid.

 

[Gib Z]

Yes there is, putting it in water :D