Pappus’s Theorem | Volumes of Revolution Made Simple (Centroid & Area Method)

Описание: Hello everyone and welcome back to Math and Engineering Made Easy!

In this session, we introduce Pappus’s Theorem (also called Pappus–Guldinus Theorem), a powerful shortcut for finding volumes of revolution. Instead of going through lengthy integrations with discs, washers, or shells, Pappus’s Theorem allows us to compute the volume directly if we know:

The area of the generating shape

The location of its centroid

With just these two pieces of information, we can determine the volume of revolution in a much faster and elegant way.

👉 In this lesson, we:

Derive Pappus’s Theorem using a simple triangle example.

Show how the centroid’s path leads directly to the volume.

Apply the theorem to a third-degree parabola and confirm the result with the method of shells.

Highlight the connection between areas, centroids, and volumes—a beautiful bridge between calculus and statics.

This theorem saves time and offers deep insight into geometry and calculus. Whether you’re studying calculus, engineering, or physics, this tool is a must-have in your problem-solving arsenal.

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