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When calculating the moment of inertial of a cylinder with the z-axis as its symmetry axis,...

When calculating the moment of inertial of a cylinder with the z-axis as its symmetry axis, why are the moment of inertia Ixx and Iyy equal? Wou;dn't you get different values? For example in the intermediate axis theorem if there is no intermediate axis how would that work?

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Moment of inertia is depend upon how the mass is distributed in a body about the axix of rotation. Since the mass along x and y direction is distributed uniformally so the moment of inertia Ixx and Iyy are equal whille body rotates about z axis.In case if we rotate the cylinder about anarbitrary axis (not about intermediate axis) then there will be changes in thevalues of  Ixx and Iyy.However If there is not intermediate axis then  Ixx and Iyy will never be same.

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