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What exactly is measured using the volume of a solid of revolution technique (ie the integral of the area)?
I wanted to know whether the integral of the cross-sectional area gives the amount of the material used or the amount of air the solid of revolution can contain (i.e. hollow volume). I am not sure, but I feel it measures the amount of material used, in which case, what do I do to find the inside volume? Subtract the material volume from the whole volume (if you get what I mean)???
1 Answer
- RicheyLv 51 decade ago
You are doing it right. its called the disc method. in mathematical gargon its:
the integral from a to b of pi * (f(x))^2 dx.
it gives you the volume.
if you did the surface of revoltion method you would get the area of material used. that formula is:
2pi * the integral from a to b of f(x) * sqrt(1 + (f ' (x))^2) dx.
Source(s): http://en.wikipedia.org/wiki/Surface_of_revolution and college
