Session 59: Volume of a Parabaloid, Revolving About y-axis

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Overview

This session introduces the "method of shells" for calculating volumes. The chosen example also illustrates the importance of understanding the units used in a mathematical model.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Volume of a Cauldron (00:16:00)

» Accompanying Notes (PDF)

From Lecture 22 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Warning about Units (00:10:00)

» Accompanying Notes (PDF)

From Lecture 22 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Volume of a Paraboloid via Disks

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Volume of Revolution via Shells

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Worked Example

 

Volume of Revolution via Washers

 

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