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**Centroid **

The point at which the total area of a plane figure or lamina is assumed to be concentrated is called centroid

**Centroid of a Line**

Centroid of an Area

**Characteristics of Centroid**

- The centroid represents the geometric center of a body
- The centroid may be located at a point that does not lie on the line/area.
- The coordinates of centroid is calculated with reference to the chosen axis
- An area can have only one centroid for all positions of the figure.
- In case of symmetric figures, centroid is located along the axes of symmetry

**Centroid Of Regular Figures**

Centre of gravity is the point about which the resultant of the whole weight of the body may be considered to act. It is denoted by G |

**A. CENTROID OF COMPOSITE FIGURES**

**Note : **If the area has a hole or cut out portion, the first moment of inertia and area must be subtracted to yield the centroid

**B. PAPPUS GULDINUS THEOREMS**

Pappus Guldinus Theorems are two theorems describing a simple way to calculate volumes (solids) and surface areas (shells) of revolution.

**First Theorem **

The surface area A of a surface of revolution generated by rotating a plane curve about an axis external to it and on the same plane is equal to the product of the arc length of the curve and the distance y traveled by its geometric centroid.

**Examples**

**Second Theorem **

The second theorem states that the volume V of a solid of revolution generated by rotating a plane area about an external axis is equal to the product of the area A and the distance y traveled by its geometric centroid

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