Question

1. what would mars diameter (6,779 km) and circumference be at the scale of your model?

diameter:
circumference:

Explanation:

Step1: Recall the scale - factor relationship

Let's assume the scale of the model is 1:x. If we know the actual diameter \(d_{actual}=6779\) km and we want to find the diameter \(d_{model}\) of the model, we need to know the scale factor. Since the scale is not given, let's assume a scale of 1:100000000 (1 cm in model represents 100000000 cm or 1000 km in real - life for example). Then \(d_{model}=\frac{d_{actual}}{scale\ factor}\).
Let's assume the scale factor \(s = 100000000\) (cm/km conversion considered). \(d_{actual}=6779\times1000\times100\) cm. \(d_{model}=\frac{6779\times1000\times100}{100000000}\) cm.

Step2: Calculate the diameter of the model

\[d_{model}=\frac{6779\times1000\times100}{100000000}=\frac{677900000}{100000000}=6.779\] cm.
For the circumference, we know that the formula for the circumference of a circle is \(C = \pi d\). First, find the actual circumference \(C_{actual}=\pi d_{actual}=\pi\times6779\) km.
For the model, \(C_{model}=\pi d_{model}\). Substituting \(d_{model} = 6.779\) cm, \(C_{model}=\pi\times6.779\approx3.14\times6.779 = 21.28606\) cm.

Answer:

Diameter: 6.779 cm
Circumference: 21.29 cm (rounded to two decimal places)