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**Pappus's Centroid Theorem**

The first theorem of Pappus states that the surface area Sof a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance d_{1}traveled by the curve's geometric centroid

(Kern and Bland 1948, pp. 110-111). The following table summarizes the surface areas calculated using Pappus's centroid theorem for various surfaces of revolution.

solid | generating curve | s | S | |

cone | inclined line segment | |||

cylinder | parallel line segment | h | r | 2Ï€rh |

sphere | semicircle | Ï€r | 2Ï€/Ï€ | 4Ï€r^{2} |

Similarly, the second theorem of Pappus states that the volume V of a solid of revolution generated by the revolution of a lamina about an external axis is equal to the product of the area A of the lamina and the distance d_{2} traveled by the lamina's geometric centroid

(Kern and Bland 1948, pp. 110-111). The following table summarizes the surface areas and volumes calculated using Pappus's centroid theorem for various solids and surfaces of revolution.

solid | generating lamina | A | V | |

cone | right triangle | |||

cylinder | rectangle | hr | Ï€r^{2}h | |

sphere | semicircle |

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30 videos|72 docs|65 tests

### Theorem 1 : Theorems of Pappus and Guldinus

- Video | 03:04 min
### Theorem 2 : Theorems of Pappus and Guldinus

- Video | 02:50 min
### Test: Theorem Of Pappus And Guldinus

- Test | 15 ques | 30 min
### Resultant of a General Distributed Force System

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### Test: Resultant Of A General Distributed Loading

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### Summary - Centroid

- Doc | 1 pages

- Test: Composite Bodies
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- Test: Centre Of Gravity
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