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