Someone who has broken an arm and has had a cast on it for months will notice a distinct shrinking of the arm once the cast is removed. why does this happen?

The answer to this question would be : If the muscles are not used they will atrophy.

Muscle cell will adapt to the intensity of the use. If someone uses the muscle to light heavyweight frequently, the muscle will become bigger so it can be used more. If the muscle is not used for a long time, it will slowly shrink.
When a broken arm had a cast, the movement of muscle is prevented so the arm muscle cannot be used until the cast removed.

The answer to that question is a