Question

The dimension 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 dimension of the building.
Also find,
The space (volume) inside a room of the model, if the space inside the corresponding room of the building is $90m^3$.

Answer 1

The dimensions of the building are calculated as below.

Length $=1\times 50$ m $=50$ m

Breadth $=0.60\times 50$ m $=30$ m

Height $=1.20\times 50$ m $=60$ m

Thus, the actual dimensions of the building are $50$ m $\times 30$ m $\times 60$ m.

Volume of the model of the building

$=90\times {\left(\frac{1}{50}\right)}^3=90\times \frac{100\times 100\times 100}{50\times 50\times 50}{cm}^3$

$=90\times 8=720{cm}^3$