Answer:
The total moment of inertia is

Step-by-step explanation:
From the question we are told that
The diameter of the core is

The mass of the core is

The mass of the shell is

The diameter of the shell is
Generally the radius of the core is

=>

=>

Generally the radius of the shell is

=>

=>

Generally the total moment of inertia is mathematically represented as

Here
is the moment of inertia of the core which is mathematically represented as
=>
=>
and
is the moment of inertia of the shell which is mathematically represented as
=>
=>
So

=>
