The diameter of Earth is 12742 kilometers. If the model that represents the Earth has diameter of 1 inch, then the scale is:

1 inch = 12742 kilometers

Expressing this as a ratio, it becomes 1:12742.

The diameter of the moon is 3474 kilometers. To determine the diameter of the model of the moon in inches, assign a variable that represent it.  Let it be x.

x inches  = 3474 kilometers

Expressing it as a ratio, it becomes x:3747.

To solve for the value of x, set the two ratios equal to each other. Take note that when used in equations, the ratio should be in fraction form.

`x/3747=1/12742`

Isolating the x, the equation becomes

`x=1/12742*3747`

`x=0.2726`  

Therefore, the diameter of the model of the moon is 0.2726 inch.