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Why does helicopter have huge rotors?

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Why does helicopter have huge rotors?

(a) Induced power is inversely proportional to rotor radius

(b) Induced power is directly proportional to rotor radius

(c) Wing loading is inversely proportional to rotor radius

(d) Wing loading is directly proportional to rotor radius

This question was posed to me during a job interview.

My question is from Helicopter Rotor and Notations in section Helicopter Dynamics of Aerodynamics

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The correct answer is (a) Induced power is inversely proportional to rotor radius

To explain: Induced power loading is proportional to square root of the rotor disk loading and inversely proportional to the rotor radius for a rotary wing in hover. Therefore, it has a large disk region of large diameter rotors for a given gross helicopter weight.

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