A model of a ship is made to a scale of 1 : 250. Find :

(i) the length of the ship, if the length of its model is 1.2 m.

(ii) the area of the deck of the ship, if the area of the deck of its model is 1.6 m².

(iii) the volume of its model, when the volume of the ship is 1 cubic kilometer.

(i) Since, the model of the ship is made to the scale of 1 : 250.

∴ K = $\dfrac{1}{250}$.

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

1.2 = $\dfrac{1}{250}$ × Actual length of the ship

Actual length of the ship = 1.2 × 250 = 300 m.

Hence, the length of the ship is 300 m.

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

1.6 = $\Big(\dfrac{1}{250}\Big)^2$ x Area of the deck of the ship

1.6 = $\dfrac{1}{62500}$ x Area of the deck of the ship

Area of the deck of the ship = 62500 x 1.6 = 100000 m²

Hence, the area of the deck of the ship is 100000 m².

(iii) Given,

Volume of ship = 1 km³ = (1000)³ m³

Let the volume of the model be x.

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

⇒ x = $\Big(\dfrac{1}{250}\Big)^3$ × 1000³

⇒ x = $\dfrac{1000 \times 1000 \times 1000}{250 \times 250 \times 250}$

⇒ x = 4 × 4 × 4

⇒ x = 64 m³.

Hence, the volume of the model of the ship is 64 m³.