Calculate the area of a solid of revolution

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So the subject title is self-descriptive. My question is how can I calculate the area of a solid of revolution with the information below:

• Cross section area (the cross section is a closed polygon without holes)
• Volume of revolution
• Volume Centroid coordinates

Take for example a rectangle revolved around the "x" axis which form a ring once is revolved. Data for the example:

• Cross section (rectangle):  368.97
• Volume of revolution: 1313668.59513298                    
• Volume Centroid coordinates: (921.45, 1.36117994286124e-13, -2.26863323810207e-14)            

Any examples are welcomed.