3. A cylindrical steel pulley is shown on Figure Q3. The inner radius of the hollow cylinder is 30 mm, and the outer radius is 50 mm. There are eight equally spaced holes, each with a radius of 5 mm, and their centres located at a distance of 40 mm from the centre of the pulley. The length of the pulley is 100 mm. The density of steel is equal to 7800 Kg/m$^3$.
(a) Determine the mass of the pulley.
(b) Determine the moment of inertia of the pulley about the axis passing through the centre of the pulley.
Axis of rotation
Figure Q3.