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Applications of Integrals: Moments and Centers of Mass: Example 5: Theorem of Pappus

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First published at 18:59 UTC on March 21st, 2019.

#mathematics
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MES

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In this video I go over an example on applying the Theorem of Pappus, which I covered in my last video, in determining the volume of a torus which is formed by rotating a circle about a line. This shape is simply a round ring or a donut. Applying Pappus's Theorem allows us to easily solve for the volume of the torus, which is simply the area of the circle multiplied by the distance the centroid of the circle travels around the line, which is the same as the circumference of the circle with radius being equal to the distance from the line to the centroid of the circle. This is a remarkably simple way of determining the volume and as I will cover in my next video, it is far easier than having to solve for the volume using basic integration techniques. So stay tuned for that!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104709&authkey=!AI8NZsC6OOdsJD4&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-moments-and-centers-of-mass-example-5-theorem-of-pappus

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