Roy made a model of his yacht with a scale of 1 : 40.

1. Convert the actual length to centimetres and apply the scale factor.

Scale $1:40$ means
$\text{model length} : \text{actual length} = 1:40.$
Actual length $=12.5\text{ m}=1250\text{ cm}$.
$\text{model length}=\frac{1250}{40}=31.25\text{ cm}$

1. Find the actual surface area using the area scale factor.

The scale of model : actual is $1:40$.

Area scale factor from model to actual:
$40^2=1600$

Actual surface area:
$937.5\times1600=1\,500\,000\text{ cm}^2$

2. Convert the actual surface area from square centimetres to square metres.

Since $1\text{ m}^2=10\,000\text{ cm}^2$,
$1\,500\,000\text{ cm}^2=\frac{1\,500\,000}{10\,000}=150\text{ m}^2$

3. Compare the two painting options and choose the cheaper option.

Option A costs $1000.

Option B costs:
$150\times5.50=825$
So Option B costs $825.

Since $825 < \1000, Roy should select Option B.