When we generate solid by rotating a curve around an axis, we use "slabs" of cylinders to approximate the volume of this solid of revolution. When we want the find the surface area, we instead use "slabs" of conical frustums (ie. the slope of the differential length of curve is taken into consideration). Why is this? The way I see it: When find the area under a curve, we approximate using rectangles. If you were to rotate the curve along with those rectangles, you generate approximating cylinders which can be used to find the volume. So why is it different when trying to find surface area? I've tried to find the surface area of a sphere by using cylinders and not the frustums and obtained the correct surface area formula.