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

(i) If the length of the model is 4m, find 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, find the volume of the ship in m³.

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

∴ K (Scale factor) = 200.

Actual length of the ship = k × (the length of model) = 200 × 4 = 800 m.

Hence, the length of the ship is 800 m.

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

Let area of deck of model be x m².

$\Rightarrow 160000 = (200)^2 \times x \\[1em] \Rightarrow x = \dfrac{160000}{200 \times 200} \\[1em] \Rightarrow x = 4.$

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

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

Given, volume of model = 200 litres = $\dfrac{200}{1000} m^3 = 0.2 m^3$.

Putting value in above equation we get,

$= (200)^3 \times 0.2 \\[1em] = 8000000 \times 0.2 \\[1em] = 1600000$

Hence, the volume of the model of the ship is 1600000 m³.