The scale factor for a model is 5cm= m model: 9.5cm actual : 30.5m

We are given dimensions of model and actual figure.

model: 9.5cm actual : 30.5m.

We need to find the length of actual shape for the scale factor 5cm.

Let us assume actual length be x m.

Let us set a proportion now.

5 : x = 9.5 : 30.5

Let us convert proportion into fractions.

[tex]\frac{5}{x}=\frac{9.5}{30.5}[/tex]

On cross multiplying, we get

9.5x = 5× 30.5

9.5x = 152.5.

On dividing both sides by 9.5, we get

[tex]\frac{9.5x}{9.5}=\frac{152.5}{9.5}[/tex]

x=16.05.

Therefore, the scale factor for a model is 5cm= 16.05 m.