Applications of Integrals: Moments and Centers of Mass: Example 5: Theorem of Pappus
1,371 views · Published 27 May 2016 · 8:04 · Indexed 20 September 2026
Channel: Math Easy Solutions · 2016 · Education
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 Related Videos: Moments and Centers of Mass: Theorem of Pappus: https://youtu.be/TLxmMLFC8tc Moments and Centers of Mass: Example 4: x and x^2: https://youtu.be/NSE92mZgz7A Moments and Centers of Mass: Region Bounded by 2 Curves: https://youtu.be/D-9tS_3XvLM Moments and Centers of Mass: Example 3: cos(x): https://youtu.be/fvvVqhzmT4s Moments and Centers of Mass: Example 2: Semi-Circle: https://youtu.be/vfCMuvqOCFM Moments and Centers of Mass: Example 1: https://youtu.be/55jrfODcbWY Moments and Centers of Mass: Introduction: https://youtu.be/lLSo5Hck6FM Hydrostatic Pressure and Force: Example 2: Force on a Drum: https://youtu.be/8tZ86Iw68l8 Hydrostatic Pressure and Force: Example 1: Force on a Dam: https://youtu.be/Gr5H4icS4CQ Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg Simplified Filter Criteria: A Dam Filter Example: http://youtu.be/yGEeYAb4Olw Soil Mechanics 101 - Phase Relations: http://youtu.be/DtKheQcL2BU Types of Tailings Embankments: Upstream, Downstream and Centerline Construction Methods: http://youtu.be/1wm1XR6z-QE Buoyancy - What is Archimedes' Principle and it's Proof: http://youtu.be/mXzccaH2KN . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps
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