Find the moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder.

Explanation

To find the moment of inertia of a solid cylinder of mass \( M \) and radius \( R \) about a line parallel to the axis of the cylinder and on the surface of the cylinder, we can follow these steps:

### Step 1: Identify the Axis of Rotation
We need to calculate the moment of inertia about a line that is parallel to the axis of the cylinder and located on its surface. This line is at a distance \( R \) (the radius of the cylinder) from the central axis of the cylinder.

### Step 2: Use the Parallel Axis Theorem
The Parallel Axis Theorem states that the moment of inertia \( I \) about any axis parallel to an axis through the center of mass is given by:
\[
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