Question

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

1. The length of the model of the ship is 2 m. Calculate the length of the ship.
2. The area of the deck of the ship is 180,000 m². Calculate the area of the deck of the model.
3. The volume of the model is 6.5 m³. Calculate the volume of the ship.

Answer 1

i. Scale factor k = `1/300`

Length of the model of the ship = k × Length of the ship 

`=> 2 = 1/300 xx "Length of the ship"`

`=>` Length of the ship = 600 m

ii. Area of the deck of the model = k² × Area of the deck of the ship

`=>` Area of the deck of the model = `(1/300)^2 xx 180,000`

= `1/90000 xx 180,000`

= 2 m²

(iii) Volume of the model = k³ × Volume of the ship

`=> 6.5 = (1/300)^3 xx "Volume of the ship"`

`=>` Volume of the ship = 6.5 × 27000000 = 175500000 m³