The general formula for the moment of inertia is…

(1)

The object you have proposed is a sort of cilinder that i suppose homogeneous and of height . In this case the (1), developped in cilindrical coordinates, becomes…

(2)

The first integral in (2) gives…

For the second integral in (2) you have to keep in mind that…

… so that…

The requested moment of inertia so is…

In case of a ‘perfect cilinder’ the moment of inertia would be…

… and that is not a surprise…

Kind regards