A model of a ship is made to a scale of $1 : 200$.
- The length of the model is $4 \; m$. Calculate the length of the ship.
- The area of the deck of the ship is $160000 \; m^2$. Find the area of the deck of the model.
- The volume of the model is $200$ liters. Calculate the volume of the ship in meter cube.
Scale of model ship is $\;$ $1 : 200$
i.e. $\;$ scale factor $= k = \dfrac{1}{200}$
- Length of $1 \; m$ in the model $= k \times$ the actual length of ship
$\implies$ $4 \; m = \dfrac{1}{200} \times$ the actual length of ship
$\implies$ the actual length of ship $= 200 \times 4 = 800 \; m$ - Area of $1 \; m^2$ in the model $= k^2 \times$ the actual area of ship
$\implies$ Area of the deck of the model $= \left(\dfrac{1}{200}\right)^2 \times 160000$
$\implies$ Area of the deck of the model $= 4 \; m^2$ - $1$ liter $= 0.001 \; m^3$
$\therefore \;$ $200$ liter $= 200 \times 0.001 = 0.2 \; m^3$
i.e. $\;$ Volume of model $= 0.2 \; m^3$
Volume of $1 \; m^3$ in the model $= k^3 \times$ the actual volume of ship
$\implies$ $0.2 \; m^3 = \left(\dfrac{1}{200}\right)^3 \times$ actual volume of ship
$\implies$ actual volume of ship $= 0.2 \times 8000000 = 1600000 \; m^3$