A model of a ship is made to a scale 1 : 300.

(i) The length of the model of the ship is 2 m. Calculate the length of the ship.

(ii) The area of the deck of the ship is 180000 m². Calculate the area of the deck of the model.

(iii) The volume of the model is 6.5 m³. Calculate the volume of the ship.

(i) Given,

Scale factor (k) = 1 : 300 = $\dfrac{1}{300}$

$\phantom{\Rightarrow} \dfrac{\text{Length of model of ship}}{\text{Length of ship}} = k \\[1em] \Rightarrow \dfrac{2}{\text{Length of ship}} = \dfrac{1}{300} \\[1em] \Rightarrow \text{Length of ship} = 2 \times 300 = 600 \text{ m}.$

Hence, length of ship = 600 m.

(ii)

$\phantom{\Rightarrow} \dfrac{\text{Area of deck of model}}{\text{Area of deck of ship}} = k^2 \\[1em] \Rightarrow \dfrac{\text{Area of deck of model}}{180000} = \dfrac{1}{300} \times \dfrac{1}{300} \\[1em] \Rightarrow \text{Area of deck of model} = 180000 \times \dfrac{1}{90000} = 2 \text{ m}^2.$

Hence, area of deck of model = 2 m².

(iii)

$\Rightarrow \dfrac{\text{Volume of model of ship}}{\text{Volume of ship}} = k^3 \\[1em] \Rightarrow \dfrac{6.5}{\text{Volume of ship}} = \Big(\dfrac{1}{300}\Big)^3 \\[1em] \Rightarrow \text{Volume of ship} = 6.5 \times (300)^3 = 6.5 \times 27000000 \text{ m}^3 \\[1em] = 175500000 \text{ m}^3.$

Hence, volume of ship = 175500000 m³.