We know that the moment of inertia for hoop with radius R is mR2. We can divide cylinder into thin concentric hoops of thickness dR.

Density = Mass per unit volume

Density = dm / dV

where:Lets assume height of the cylinder is h.

þ; - Density

dm - Mass of a ring or radius R

dV - Volume of a ring or radius R

we have

We can obtain moment of inertia by integrating over all these hoops

Cylinder has uniform density, where þ = constant

Volume of this cylinder is

Mass M is

since

Moment of inertia for hollow cylinder is