A model of a ship is made to a scale of 1 : 160. 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 deck of its model is 1.2 m².

(iii) the volume of the ship, if the volume of its model is 1.2 m³.

Given,

Scale of model = 1 : 160

Scale factor (k) = $\dfrac{1}{160}$

(i) By formula,

⇒ Length of model = Scale factor × Length of ship

⇒ 1.2 = $\dfrac{1}{160}$ × Length of ship

⇒ Length of ship = 1.2 × 160 = 192 m.

Hence, length of ship = 192 m.

(ii) By formula,

⇒ Area of model = (Scale factor)² × Area of ship

⇒ 1.2 = $\Big(\dfrac{1}{160}\Big)^2$ × Area of ship

⇒ 1.2 = $\dfrac{1}{160 \times 160}$ × Area of ship

⇒ Area of ship = 1.2 × 160 × 160 = 30720 m².

Hence, area of ship = 30720 m².

(iii) By formula,

⇒ Volume of model = (Scale factor)³ × Volume of ship

⇒ 1.2 = $\Big(\dfrac{1}{160}\Big)^3$ × Volume of ship

⇒ 1.2 = $\dfrac{1}{160 \times 160 \times 160}$ × Volume of ship

⇒ Volume of ship = 1.2 × 160 × 160 × 160 = 49,15,200 m³.

Hence, volume of ship = 49,15,200 m³.