What is not the condition for the equilibrium in three dimensional system of axis for the bodies for which this theorem is going to be applied?

The Theorem of Pappus and Guldinus, also known as Pappus's centroid theorem, is a mathematical theorem that deals with the surface areas and volumes of solids and surfaces of revolution. The theorem states that the volume of a solid of revolution is equal to the area of its base multiplied by the circumference of the circle in which the center of gravity of that figure is revolved.  The theorems are attributed to Pappus of Alexandria and Paul Guldin. Pappus's statement of the theorem first appeared in print in 1659, but it was known before by Kepler in 1615 and by Guldin in 1640.  The... Show more

The Theorem of Pappus and Guldinus, also known as Pappus's centroid theorem, is a mathematical theorem that deals with the surface areas and volumes of solids and surfaces of revolution. The theorem states that the volume of a solid of revolution is equal to the area of its base multiplied by the circumference of the circle in which the center of gravity of that figure is revolved. 
The theorems are attributed to Pappus of Alexandria and Paul Guldin. Pappus's statement of the theorem first appeared in print in 1659, but it was known before by Kepler in 1615 and by Guldin in 1640. 
The theorems can be applied to find the surface area and volume of composite shapes. To find the surface area, the generating curves for each shape are identified and revolved around a non-intersecting axis. Then, the centroid is located for each curve. 

Related Test: Engineering Mechanics Practice Test: Centre of Gravity and Centroid

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