Question

A model of a high-rise building is made to a scale of 1 : 50.

1. If the height of the model is 0.8 m, find the height of the actual building.
2. If the floor area of a flat in the building is 20 m², find the floor area of that in the model.

Answer 1

Given: Scale factor (model : actual) = 1 : 50

(i)

Height of model = 0.8 m

Actual height = 0.8 × 50

∴ Actual height = 40 m

(ii)

For similar figures,

Area ratio = (scale factor)²

= (1 : 50)²

= 1 : 2500

Given actual area = 20 m²

Model area = `20/2500`

Model area = 0.008 m²

∴ Floor area in model = 0.008 m²