What exactly is measured using the volume of a solid of revolution technique (ie the integral of the area)?

Question

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)???

Richey · Answer

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.

What exactly is measured using the volume of a solid of revolution technique (ie the integral of the area)?

Related Questions

Trending Questions