In a model for Ms. Fowler’s science class, the diameter of the Earth is 12,756 km and the model is 0.9 mm. The diameter of Jupiter is 142,980 km or 10.4 mm. Are the model's diameter's proportional to the actual dimensions of the solar system?(1 point)
To determine if the model's diameter is proportional to the actual dimensions of the solar system, we need to compare the ratios of the model's diameter to the actual diameter for both the Earth and Jupiter.
For the Earth:
Model-to-actual diameter ratio = 0.9 mm / 12,756 km
For Jupiter:
Model-to-actual diameter ratio = 10.4 mm / 142,980 km
To compare these ratios, we need to convert the units to be consistent. Let's convert the model-to-actual diameters to the same units of measure, either mm or km.
For the Earth:
Model-to-actual diameter ratio = 0.9 mm / 12,756 km * 1,000,000 mm/km
Model-to-actual diameter ratio = 0.9 * 1,000,000 / 12,756 mm/mm
Model-to-actual diameter ratio = 70.573 mm/mm
For Jupiter:
Model-to-actual diameter ratio = 10.4 mm / 142,980 km * 1,000,000 mm/km
Model-to-actual diameter ratio = 10.4 * 1,000,000 / 142,980 mm/mm
Model-to-actual diameter ratio = 72.654 mm/mm
Comparing these ratios, we can see that the model's diameter is proportional to the actual dimensions of the solar system for both the Earth and Jupiter.