Originally Posted by

**dude_500** I understand that to find the surface area of revolution you integrate over the bounds using 2 pi f(x) arc length dx, however I do not understand why I can't simply use 2 pi f(x) dx as the integrand since this is just calculating infinite circumferences and multiplying by the height, dx, of the infinitely small cylinder created. This works for calculating volumes using areas and then multiplying by the infinitely small height, and I don't understand why I can't do the same by finding the single dimensional length of the circumference and then multiplying by the height, dx.