Models of earth, moon, and mars are proportionally sized in a 1:300 million scale. Earth and moon are really 384,400 km (238,855 mi) apart. Using our 1:3 x 108 scale, earth and moon would be how far apart? [part a = 5 pts; part b = 5 pts] (a) _ cm (b) __ in [give your answer in centimeters and inches. Round to 1 decimal. Hint: use proportions; remember that 2.54 cm = 1 in.] show your work (round each answer to 1 decimal): [20 pts total] [work = 10 pts]

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Sicista Sicista · Answer 1 · 2018-09-22T20:55:59+02:00

The answers are: (a) 128.1 cm (b) 50.4 inch

Explanation

Scale ratio is..... [tex]1: (3*10^8)[/tex]

It means the ratio of the scaled distance to the real distance is [tex]1: (3*10^8)[/tex]

Given that, Earth and Moon are really 384,400 km apart.

Suppose, the scaled distance between Earth and Moon is [tex]x[/tex] km.

So the equation according to the ratio will be ......

[tex]\frac{x}{384400}=\frac{1}{3*10^8}\\ \\ x= \frac{384400}{3*10^8}=0.00128133.....[/tex]

As, 1 km = 100000 cm

So, [tex]0.00128133..... km = (0.00128133.....*100000)cm = 128.133... cm[/tex] ≈ 128.1 cm

Now, 2.54 cm = 1 inch

So, [tex]128.1 cm = \frac{128.1}{2.54} inch = 50.4[/tex] inch

Thus, using [tex]1: 3*10^8[/tex] scale, Earth and Moon would be 128.1 cm or 50.4 inch apart.