Pappus-Guldinus Theorems

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Theorem

There are two theorems that bear the name Pappus-Guldinus Theorem:


First Pappus-Guldinus Theorem

Let $C$ be a plane figure that lies entirely on one side of a straight line $\LL$.

Let $S$ be the solid of revolution generated by $C$ around $\LL$.


Then the volume of $S$ is equal to the area of $C$ multiplied by the distance travelled by the centroid of $C$ around $\LL$ when generating $S$.


Second Pappus-Guldinus Theorem

Let $C$ be a plane figure that lies entirely on one side of a straight line $L$.

Let $S$ be the solid of revolution generated by $C$ around $L$.

Then the surface area of $S$ is equal to the perimeter length of $C$ multiplied by the distance travelled by the centroid of $C$ around $L$ when generating $S$.


Also known as

These theorems are also known as:

the Pappus Centroid Theorems
Guldinus' Theorems.


Also see


Source of Name

This entry was named for Pappus of Alexandria and Paul Guldin.


Sources