| ES-190 Theorems of Pappus |
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The theorems of Pappus may be used to find the surface of revolution and volume of revolution for bodies generated by revolving a plane curve about an axis. |
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THEOREM I: The area of a surface of revolution is equal to the length of the generating curve times the distance traveled by the centroid while the surface is being generated. |
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| This is shown in the diagram... |
We can write this in equation form as where L is the length of the curve. |
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THEOREM II: The volume of a body of revolution is equal to the generating area times the distance traveled by the centroid of the are while the body is generated. |
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This is shown in the diagram below: |
We can write this in equation form as where A - generating area. |