In a scale model of the Solar System, if the Sun is represented by a ball with a diameter of about 8 inches, about how large would the Earth be? A. the size of a grapefruit B. the size of an apple C. the size of a marble D. the size of a popcorn seed

size of popcorn seed may meet the scaled earth size of x = 0.07312 in.

Explanation:

Given:-

- The diameter of actual sun, Ds = 1.3927 * 10^6 km

- The diameter of model sun ball, ds = 8 in

- The diameter of the actual earth, De = 12,742 km

Find:-

How large would be the earth model

Solution:-

- We can use the actual diameters of the earth and sun to develop the ratio of earth diameter to that of sun. The direct ratio can be used to model the diameter of earth for the scale model

Sun Earth

Actual : 1392700 km 12,742 km

Scale : 8 in x

- Use direct relations and solve for x:

x = (8 in) * (12,742 km) / (1392700 km)

x = 0.07312 in.

- From the given options apple, grapefruit and marble diameters are larger than 1 inch. So only the size of popcorn seed may meet the scaled earth size of x = 0.07312 in.

Answer: D. The size of a popcorn seed