Question

A model of a ship is made to a scale of 1 : 250. Calculate:

1. the length of the ship, if the length of the model is 1.6 m.
2. the area of the deck of the ship, if the area of the deck of the model is 2.4 m².
3. the volume of the model, if the volume of the ship is 1 km³.

Answer 1

The given scale factor is 1 : 250.

(i) Length of the ship:

Given that the length of the model is 1.6 m.

Actual length = Model length × 250

Actual length = 1.6 × 250

∴ Actual length = 400 m

Hence, the length of the ship = 400 m.

(ii) Area of the deck of the ship:

Given the area of the model deck is 2.4 m². We use the square of the scale factor for area.

Actual area = Model area × (250)²

Actual area = 2.4 m² × 62,500

Actual area = 150,000 m²

Hence, Area of the deck = 150,000 m²

(iii) Volume of the model:

Given that the volume of the ship is 1 km³. We use the cube of the scale factor for volume.

First, converting 1 km³ to meters:

1 km³ = (1000 m)³ = 1,000,000,000 m³

Now, let’s calculate the model volume:

Model volume = `"Actual volume"/(250)^3`

Model volume = `((1000  m)/250)^3`

Model volume = (4 m)³

∴ Model volume = 64 m³