If a curve is rotated 2Pi about the x-axis, a solid is formed. The volume of revolution is Pi int y^2 dx The surface area of revolution is 2Pi int y ds. I understand the formulae, what I dont understand is why for the surface area it is 'ds' instead of dx. ...surely you are finding the circumference of lots of circles, adding them up along the x-axis? That is what happens with vol of revolution where you adding up the areas of lots of circles along the x-axis....so you sum along the axis and thus should be using dx? There is a flaw in my understanding...what is it?