A model of a ship is made to a scale of 1 : 200.

(i) If the length of the model is 4 m, calculate the length of the ship.

(ii) If the area of the deck of the ship is 160000 m², find the area of the deck of the model.

(iii) If the volume of the model is 200 litres, calculate the volume of the ship in cubic metres.

(i) Since, the model of the ship is made to the scale of 1 : 200.

∴ K = $\dfrac{1}{200}$.

Length of model ship = k × (Actual length of the ship)

4 = $\dfrac{1}{200}$ × Actual length of the ship

Actual length of the ship = 4 × 200 = 800 m.

Hence, the length of the ship is 800 m.

(ii) Area of the deck of the model = k² × (Area of the deck of the ship)

Let area of deck of model be x.

⇒ x = $\Big(\dfrac{1}{200}\Big)^2$ × (160000)

⇒ x = $\dfrac{1}{40000}$ × (160000)

⇒ x = 4 m².

Hence, the area of the deck of model is 4 m².

(iii) Given,

Volume of model = 200 litres = $\dfrac{200}{1000} \text{ m}^3 = 0.2 \text{ m}^3$

Volume of the model = k³ × (Volume of the ship)

0.2 = $\Big(\dfrac{1}{200}\Big)^3$ × Volume of the ship

0.2 = $\dfrac{1}{8000000}$ × Volume of the ship

Volume of the ship = 8000000 × 0.2 = 1600000.

Hence, the volume of the ship is 1600000 m³.