The dimensions of the model of a multistorey building are 1 m × 60 cm × 1.25 m. If the model is drawn to a scale 1 : 60, find the actual dimensions of the building in meters. Find:

(i) the floor area of a room of the building, whose area in the model is 250 cm²,

(ii) the volume of the room in the model, whose actual volume is 648 cubic metres.

(i) Given,

Scale factor (k) = 1 : 60 = $\dfrac{1}{60}$

Dimensions of model = l × b × h = 1 m × 60 cm × 1.25 m.

= 1 m × 0.60 m × 1.25 m.

We know that,

Model dimensions = k × Actual dimension

$\text{Actual length} = \dfrac{\text{ Model length}}{k} \\[1em] = \dfrac{1}{\dfrac{1}{60}} \\[1em] = 60 \text{ m}. \\[1em] \text{Actual breadth} = \dfrac{\text{ Model breadth}}{k} \\[1em] = \dfrac{0.60}{\dfrac{1}{60}} \\[1em] = 0.60 \times 60\\[1em] = 36 \text{ m}. \\[1em] \text{Actual height} = \dfrac{\text{ Model height}}{k} \\[1em] = \dfrac{1.25}{\dfrac{1}{60}} \\[1em] = 1.25 \times 60 \\[1em] = 75 \text{ m}.$

Actual dimensions (in meters) = 60 m × 36 m × 75 m.

By formula,

Floor area of model room = k² × Floor area of building room

250 = $\dfrac{1}{60} \times \dfrac{1}{60}$ × Floor area of building room

Floor area of building room = 60 × 60 × 250 cm²

= 900000 cm²

= $\dfrac{900000}{10000}$ m².

= 90 m².

Hence, length = 60m, breadth = 36 m, height = 75m, floor area of a room of the building = 90 m².

(ii) By formula,

Volume of a room of model = k³ × Volume of a room of building

= $\dfrac{1}{60} \times \dfrac{1}{60} \times \dfrac{1}{60} \times 648$

= $\dfrac{1}{60} \times \dfrac{1}{60} \times \dfrac{1}{60} \times 648$ m³

= 0.003 x 100 x 100 x 100 cm³

= 3000 cm³.

Hence, volume of a room in model = 3000 cm³.