Second Pappus-Guldinus Theorem

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 $S$.

Proof

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Also known as

This result is also known as:

Pappus's Centroid Theorem for Surface Area

the Second Guldinus Theorem.

Also see

• First Pappus-Guldinus Theorem

Source of Name

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

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Pappus' theorems (1)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pappus' theorems (1)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Pappus' Theorems