Question

Micheal makes a model to show the distances between the sun and planets. Earth is 1.50 x 10^11m from the sun. The distance on earth the model is 37.5cm. What is the ratio of the length of the model to the actual distance?

A. 1:4 x 10^10
B. 1:4
C. 1:400 x 10^10
D. 1:400

Answer 1

The ratio of the length of the model to the actual distance, with Earth being 1.50 x 10^11 meters from the Sun and the model distance being 37.5cm, is 1:4 x 10^10.

Step-by-step explanation:

The student is asking how to determine the ratio of the length of a solar system model to the actual distances between the Sun and the planets. Specifically, the model represents Earth's distance from the Sun as 37.5cm, while the actual distance is 1.50 x 10^11 meters.

To find this ratio, we need to convert the actual distance from meters to centimeters by multiplying by 100 (since 1 meter = 100 centimeters). Therefore, the actual distance in centimeters is 1.50 x 10^11 meters x 100 = 1.50 x 10^13 centimeters. Now, we can set up the ratio as follows:

Model distance: Actual distance = 37.5cm : 1.50 x 10^13 cm

Dividing both sides of the ratio by 37.5cm gives us:

1 : (1.50 x 10^13 cm / 37.5cm) = 1 : 4 x 10^10

Thus, the ratio of the length of the model to the actual distance is 1:4 x 10^10.