How do I calculate the second moment of a solid cylinder?

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To calculate the second moment of a solid cylinder, one must set up an integral using polar or cylindrical coordinates. The differential area element, dA, can be expressed in these coordinates, which simplifies the integration process. The limits of integration should be defined based on the cylinder's dimensions, particularly considering cases where the thickness is much smaller than the radius or vice versa. Understanding these parameters is crucial for accurately determining the second moment. Proper setup of the integral will lead to the correct calculation of the second moment for the solid cylinder.
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can someone help me show the second moment of solid cylinder?

the diagram and the equation is in the attached picture.
 

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Please try to set up the integral. What is dA in polar or cylindrical coordinates? What of the limits of integration?

Also, I suspect the problem is for the case where t << R or conversely where R >> t.
 

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