Question

A model of a ship is made to a scale of 3:400
The surface area of the model is 7200 cm
Calculate, in m?, the surface area of the ship.​

Answer 1

Given:

Model : Ship = 3 : 400

Surface area of the model = 7200 cm²

To Find:

Surface area of the actual ship in m²

Let's start with the map scale given:

Model : Ship = 3 : 400

We start by adding in a unit. Usually we choose the units associated with the model:

Model : Ship = 3 cm : 400 cm

Now, according tot the question, we know that the actual ships is in m:

Model : Ship = 3 cm : 400 ÷ 100 m

Model : Ship = 3 cm : 4 m

The question asked for surface area, so the units have to be in squares:

Model : Ship = (3 cm)² : (4 m)²

Model : Ship = 9 cm² : 16 m²

Now, that we have the units set correctly according to the question requirement, we will find 1 unit of the model:

Model : Ship = 9 cm² : 16 m²

Model : Ship = 9÷9 cm² : 16÷9 m²

Model : Ship = 1 cm² : 16/9 m²

Finally, we can find the required units by multiplying both sides with the required units:

Model : Ship = 1 cm² : 16/9 m²

Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²

Model : Ship = 7200 cm² : 12800 m²

Answer: The surface area of the ship is 12800 m²

Answer 2

Given :

Scale i.e. ratio of model to the actual dimension of ship:

= 3 : 400

Surface area of the model of the ship:

= 7200 cm

To Find :

The surface area of the ship in m will be  = ?

Solution :

∴For the 3 cm of model length , the actual length:

= 400 cm

So , for 1 cm of model length , the actual length :

= $\frac{400}{3}$ cm

⇒For 7200 cm of model length , the actual length:

=

 $7200\times \frac{400}{3} \\=2400 \times 400\\=960000 cm$

∴1 cm = $\frac{1}{100} m$

⇒960000  cm = $\frac{960000}{100} \\=9600 m$

So the surface area of the ship in m is 9600 m.