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

(i) the length of the ship, if the length of model is 1.6 m.

(ii) the area of the deck of the ship, if the area of the deck of model is 2.4 m².

(iii) the volume of the model, if the volume of the ship is 1 km³.

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

∴ K (Scale factor) = 250.

Actual length of the ship = k × (the length of model) = 250 × 1.6 = 400 m.

Hence, the length of the ship is 400 m.

(ii) Area of the deck of the ship = k² × (Area of the deck of the model)
= (250)² x 2.4
= 250 x 250 x 2.4
= 1,50,000 m²

Hence, the area of the deck of the ship is 1,50,000 m².

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

Given, volume of ship = 1 km³ = (1000)³ m³

Let the volume of the model be x m³.

$\Rightarrow 1000^3 = 250^3 \times x \\[1em] \Rightarrow x = \dfrac{1000 \times 1000 \times 1000}{250 \times 250 \times 250} \\[1em] \Rightarrow x = 4 \times 4 \times 4 \\[1em] \Rightarrow x = 64.$

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