The area under the curve of 1/x from 1 to infinity diverges, resulting in an infinite area, as shown by the integral A = ∫(1 to ∞) (1/x) dx = ∞. In contrast, the volume of the solid of revolution formed by rotating this curve around the x-axis converges to a finite value, calculated as V = π ∫(1 to ∞) (1/x²) dx = π. This phenomenon, often perceived as paradoxical, was noted by the ancient mathematician Pappo di Alessandria. The discussion highlights the distinction between area and volume in calculus, emphasizing that infinite area can correspond to finite volume. Understanding this concept is crucial in advanced calculus and mathematical analysis.