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

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

$12.5\text{ m}=12.5\times100=1250\text{ cm}$

Scale $1:40$ means

$\text{model length}=\frac{1250}{40}=31.25\text{ cm}.$

1. Use the area scale factor to find the actual surface area in $\text{cm}^2$.

Scale of model : actual $=1:40$.

For area,
$\text{model area} : \text{actual area}=1^2:40^2=1:1600.$

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

2. Convert the actual surface area from $\text{cm}^2$ to $\text{m}^2$.

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. Calculate the cost under Option B and compare it with Option A.

Option B cost
$=150\times \$5.50=\$825.$

Option A cost $=\char36{}1000$.

Since $\char36{}825<\char36{}1000$, Option B is cheaper.