Pappus and Guldinus developed theorems to find the surface area and volume of any body of revolution. To generate the surface area, revolve a plane curve of known length around the x-axis. Consider a differential line element. When revolved, it generates a ring, which is integrated to obtain the entire surface area. The first theorem states that the area of a surface of revolution is the product of the generating curve's length and the distance the centroid of the curve travels while generating the surface. Similarly, to find the volume of revolution, a plane area is revolved around a non-intersecting axis. Consider a differential area, generating a volume element when revolved. The differential volume is then integrated to determine the entire volume. The second theorem states that the volume of a body of revolution is the product of the generating area and the distance the centroid of the area travels while generating the volume. In both cases, the formula changes accordingly if the revolution is only through an angle.