By deleting the volume of the lower bounded function, will yield out a hole in the function. The whole minus the hole: remember that since the volume is being subtracted, pug in the voluume function for the shape.
$$ V=\pi\int_a^b[v(R(x))^2-v(r(x))^2]dx $$
R(x)- the distance between the function of the upper bound and the line it perpendicular to.
r(x)- the distance between the function of the lower bound and the line it perpendicular to.