Assume I have a solid $f_1(x,y,z) = 0$ and I have another solid $f_2(x,y,z) = 0$ that fits entirely within $f_1$. If I wanted to compute the volume of the shell $V = f_1 - f_2$ I just need to do a triple iterated integral and be done with it. However, I would like to know, if $f_2$ and $f_1$ describe the same shape, but $f_2$ is just scaled, is there a simpler way of computing the volume?
For instance, if $f_2$ is defined such that I know the thickness of the shell is 0.5 everywhere, is there a simplification I can use to get the amount of material in the shell itself?