A model of a ship is made to a scale of $1 : 200$ .
(i) If the length of the model is $4 m$ , find the length of the ship.
(ii) If the area of the deck of the ship is $160000 m^{2}$ , find the area of the deck of the model.
(iii) If the volume of the model is $200$ liters, find the volume of the ship in $m^{3} . (100 l i t e r s = 1 m^{3})$ .

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Solution

Let length, area and volume of ship model be $l_{s m}, A_{s m}, V_{s m}$ respectively.
Let length, area and volume of ship be $l_{s}, A_{s}, V_{s}$ respectively

$l_{s} = {200 l}_{s m} A_{s} = {(200)}^{2} A_{s m} = 40000 A_{s m} V_{s} = {(200)}^{3} V_{s m} = 8000000 V_{s m}$

(i) $l_{s m} = 4 m \Rightarrow l_{s} = 4 \times 200 = 800 m$
(ii) $A_{s} = 160000 m^{2} \Rightarrow A_{s m} = \frac{A_{s}}{200^{2}} = \frac{160000}{40000} = 4 m^{2}$
(iii) $V_{s m} = 200 l i t e r s = 200 \times 0.001 m^{3} = 0.2 m^{3} (∵ 1 l i t e r = 0.001 m^{3}) V_{s} = V_{s m} \times {(200)}^{3} = 0.2 \times 8000000 = 1600000 m^{3}$

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