Statics: Exam 2 Review Problem 6, Theorem of Pappus Guldinus

Statics: Exam 2 Review Problem 6, Theorem of Pappus Guldinus

Exam 2 is coming up fast, and today we are tackling a topic that trips up a lot of students—the Theorem of Pappus Guldinus! In this video, we are solving Problem 6 from our Exam 2 Review series, focusing on how to find both the total Surface Area and the Volume of a complex, revolved 3D mechanical part.

Don’t let these scary-looking 3D rolled or turned shapes intimidate you! The secret to mastering Pappus Guldinus is all in the setup. I’ll show you how to take a complex 3D object, cut it in half, sketch its 2D generating cross-section shape, and break it down into simple composite segments.

For the Surface Area, we’ll analyze 5 distinct line segments, including a tricky curved quarter-circle arc where we’ll use the 2r/π centroid formula. For the Volume, we’ll divide the cross-section into a triangle, a rectangle, and a semi-circular groove that needs to be subtracted since it’s a hollow cutout. Grab your calculator, your formula sheet, and let’s ace this exam prep together!

Timestamps:

00:12 – Theorem of Pappus Guldinus Formulas

01:48 – Sketching the 2D Generating Shape

03:44 – Surface Area Calculation (5 Line Segments)

07:21 – Centroid for the Curved Quarter-Circle Arc

10:56 – Volume Calculation: Composite Areas

13:33 – Using 4r/3π Formula for Hollow Cutout

15:17 – Final Volume Solutions & Wrap-Up

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