Question

The dimensions of the model of a multistory building are 1.2m \[ \times \] 75 cm \[ \times \] 2m. If the scale factor is 1:30; find the actual dimensions of the building.
A. 23m\[ \times \]22.5m\[ \times \]60m
B. 12m\[ \times \]22.5m\[ \times \]60m
C. 17m\[ \times \]22.5m\[ \times \]60m
D. 36m\[ \times \]22.5m\[ \times \]60m

Answer 1

Hint: Firstly convert the units in meters, and to find the actual dimensions we divide the scale factor with the given dimensions in the question.

Complete step-by-step answer:
Here we are given the dimensions of the multistory building which is given in a shorter format. Now to find the actual dimensions of a building we need to amplify it with the help of our scale factor.
Given, Scale factor = \[\dfrac{1}{{30}}\]
Length of the model building = 1.2 m
Actual length= \[\dfrac{{30}}{1} \times 1.2m\]= 36 m
Breadth of the model building = 75 cm = 0.75 m
And Breadth = 75cm\[ \times \dfrac{{30}}{1}\] = 2250 cm = 22.5 m
Height of the model building = 2 m
And height = 2 m \[ \times \dfrac{{30}}{1}\]= 60m
So, we have,
Actual dimensions of the building are= 36m\[ \times \]22.5m\[ \times \]60m
Hence, option (d) is correct.

Note: Though this is an easy problem, still we have to keep in mind that the model building is always smaller than the actual one and we have to check our scale factor according to that. As the real building’s dimensions can’t ever be smaller than the model building’s dimensions.