Pappus's Theorem

Pappus's Theorem relates to the surface area generated when a shape is rotated around an external axis. It states that this surface area depends only on the shape's size and its position relative to the axis. Specifically, if you imagine a flat shape (like a triangle or a circle) and rotate it around a line outside or inside it, the surface area created can be found by multiplying the shape's area by the path it traces during rotation (its "perimeter" or boundary length). This theorem helps calculate complex surfaces of revolution by linking shape geometry to the resulting surface area.