This question is a direct demonstration of measuring by displacement. When you place the ball in the water, it displaces some of the water, pushing it out of the way. We see this as the water level rising. By subtracting the initial reading of the water volume (100 mL) from the final water volume (300 mL), we can deduce that the volume occupied by the ball is 200 mL.
Your question about whether the material the ball is made of affects the result is an excellent question, however. The process of measuring by displacement presumes that the object being measured does not interact with the fluid it is immersed in. If the ball absorbs some of the water, dissolves in the water, or has a chemical reaction with the water, any of those things would invalidate the measurement.
If you need to measure an object by displacement and the object will interact with the water, then you would have to find an alternative fluid to immerse the object in.