Final answer:
The necessary ratio for model dimensions in centimeters to kilometers of actual distance is 30 meters in the model to 30,000,000 kilometers in the actual solar system.
Step-by-step explanation:
To determine the necessary ratio for the model dimensions in centimeters to kilometers of actual distance, we need to establish a scale factor. In this case, we are given that the model diameter is 30 meters. Let's assume that the model diameter is the same as the diameter of the actual solar system. So, if the model diameter is 30 meters, and we divide every dimension by a factor of 10⁹, the actual diameter of the solar system would be 30 meters x 10⁹ = 30,000,000,000 meters. Now, let's convert the actual diameter from meters to kilometers, which is 30,000,000,000 meters ÷ 1000 = 30,000,000 kilometers. Therefore, the necessary ratio for model dimensions in centimeters to kilometers of actual distance would be 30 meters in the model to 30,000,000 kilometers in the actual solar system.