Wind power is the amount of electrical energy that can be generated by a windmill. It is important to understand the factors that affect wind power to optimize the efficiency of wind turbines and maximize their energy generation. The wind speed and the radius of the windmill's blades are two of the key factors that determine wind power.

**Wind Speed and Wind Power**
The wind speed directly affects the amount of power that can be generated by a windmill. As the wind blows faster, it exerts more force on the windmill's blades, causing them to rotate at a higher speed. This rotation generates more mechanical energy, which can be converted into electrical energy. Therefore, wind power is directly proportional to the wind speed.

**Mathematical Relationship**
The mathematical relationship between wind power and wind speed can be described by an equation. According to scientific research and empirical data, wind power is directly proportional to the cube of the wind speed. This means that if the wind speed doubles, the wind power will increase by a factor of eight (2^3). Similarly, if the wind speed triples, the wind power will increase by a factor of twenty-seven (3^3).

**Explanation of Option B**
Option B states that wind power is directly proportional to the cube of the wind speed. This is the correct answer because it accurately describes the relationship between these two variables. The cube of the wind speed represents the exponential increase in wind power as the wind speed increases. This relationship highlights the importance of harnessing high wind speeds to maximize the energy generation of windmills.

**Importance of Blade Radius**
While wind speed is a crucial factor in determining wind power, the radius of the windmill's blades also plays a significant role. The larger the radius, the more area the blades cover, resulting in a greater capture of wind energy. Therefore, wind power is also directly proportional to the radius of the blades. However, it is important to note that the relationship between wind power and blade radius is not as pronounced as the relationship between wind power and wind speed.

In conclusion, wind power is directly proportional to the cube of the wind speed. This relationship highlights the exponential increase in wind power as the wind speed increases. Additionally, the radius of the windmill's blades also affects wind power, although to a lesser extent. By understanding these relationships, wind turbine designers and operators can optimize the efficiency and energy generation of windmills.