Question

A model of a ship is made to a scale of $1:200$.
(i) If the length of the model is $4m$, find the length of the ship.
(ii) If the area of the deck of the ship is $160000m^2$, 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 $m^3.(100liters=1m^3)$.

Answer 1

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

Let length, area and volume of ship be $l_s,A_s,V_s$ respectively

$l_s={200l}_{sm}{A}_s={\left(200\right)}^2{A}_{sm}=40000A_{sm}{V}_s={\left(200\right)}^3{V}_{sm}=8000000V_{sm}$

(i) $l_{sm}=4m\Rightarrow l_s=4\times 200=800m$

(ii) $A_s=160000m^2\Rightarrow A_{sm}=\frac{A_s}{{200}^2}=\frac{160000}{40000}=4m^2$

(iii) $V_{sm}=200liters=200\times 0.001m^3=0.2m^3(\because 1liter=0.001m^3)V_s=V_{sm}\times {\left(200\right)}^3=0.2\times 8000000=1600000m^3$