Question

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]

Answer 1

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

Step-by-step explanation

Scale ratio is.....
`1: (3*10^8)`

It means the ratio of the scaled distance to the real distance is
`1: (3*10^8)`

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

Suppose, the scaled distance between Earth and Moon is
`x` km.

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

`(x)/(384400)=(1)/(3*10^8)\\ \\ x= (384400)/(3*10^8)=0.00128133.....`

As, 1 km = 100000 cm

So,
`0.00128133..... km = (0.00128133.....*100000)cm = 128.133... cm` ≈ 128.1 cm

Now, 2.54 cm = 1 inch

So,
`128.1 cm = (128.1)/(2.54) inch = 50.4` inch

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