Question

The dimensions of the model of a multistoreyed building are 1 m by 60 cm by 1.20 m. If the scale factor is 1 : 50, find the actual dimensions of the building. 

Also, find: 

1. the floor area of a room of the building, if the floor area of the corresponding room in the model is 50 sq. cm.
2. the space (volume) inside a room of the model, if the space inside the corresponding room of the building is 90 m³.

Answer 1

The dimensions of the building are calculated as below.

Length = 1 × 50 m = 50 m

Breadth = 0.60 × 50 m = 30 m

Height = 1.20 × 50 m = 60 m

Thus, the actual dimensions of the building are 50 m × 30 m × 60 m.

i. Floor area of the room of the building

= `50 xx (50/1)^2`

= 125000 cm²

= `(125000)/(100 xx 100)`

= 12.5 m²

ii. Volume of the model of the building

`90(1/50)^3 = 90 xx (1/50) xx (1/50) xx (1/50)`

= `90 xx ((100xx100xx100)/(50xx50xx50)) cm^3`

= 720 cm³