Q. 15 Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius, about an axis passing through their axes of symmetry?

Hint: Use moment of inertia, I=Σmiri2.
Step 1: Interpret the answer.
 
The moment of inertia of a body is given by I=Σmiri2 [sum of moment of inertia of each constituent particles]
 
All the mass in a cylinder lies at distance R from the axis of symmetry but most of the mass of a solid sphere lies at a smaller distance than R.