The model of a building is constructed with the scale factor 1 : 30

Trigonometry (10)

The model of a building is constructed with the scale factor 1 : 30.

  1. If the height of the model is 80 cm, find the actual height of the building in meters.
  2. If the actual volume of a tank at the top of the building is 27 m3, find the volume of the tank on the top of the model.

Answer

K = 1 / 30

(i) Height of model = 1/ 30 × Actual height of the building = 30 × 80 cm = Actual height of the building

Actual height of the building = 2400 cm = 24 m

OR

1: 30 = 80 : x (where x is the actual height of the building)

∴ x = 2400 cm = 24 m.

(ii) Volume of the tank on the top of the model

= (1/k)3 × Actual volume of tank at the top of the building

=1×27 / 30×30×30 m3

=27×100×100×100 / 30×30×30 cm3

= 1000 cm3

Exam Year: 2019