@LostInParadise The shell method works too. You can either integrate the areas of circular disks stacked longitudinally, or the areas of cylindrical shells nested along a radius. They are both useful approaches. Volumes or surfaces of revolution are 3-dimensional, but perfect circular symmetry reduces them to functions of 2 variables. So you integrate some kind of 2-dimensional region with respect to a 3rd orthogonal axis. Properly expressing boundaries is usually the tricky part.
Regions bounded by straight lines before rotation give rise to some combination of cylinders & cones, as @prasad points out, so you could just use solid geometry volume formulas. Functions in general, however, require the power of calculus to calculate volumes & areas, as illustrated by @LostInParadise‘s setup above.
In my day the book was Kreyszig Advanced Engineering Mathematics, apparently still in print today.