Question

The model of building is constructed with the scale factor 1:30.
(i)If the height of the model is 80 cm, find the actual height of the building in metres.
(ii)If the actual volume of the tank at the top of the building is 27 $m^3$. Find the volume of the tank on the top of the model.

Answer 1

Hint: Use the ratio 1:30 where 1 is model dimension and 30 as actual dimension and follow the question and solve accordingly.

Complete step-by-step answer:
Scale = 1:30.
(i)Height of the model = 80 cm
Let the actual height = x
\[\dfrac{1}{{30}} = \dfrac{{80}}{x}\]
\[ \Rightarrow x = 80 \times 30\]cm
\[ = 2400\]cm
\[ = 24\]m

(ii)Actual volume of tank = 27 $m^3$
Let the volume of the tank at the top of the model = x.
\[{\left( {\dfrac{1}{{30}}} \right)^3} = \left( {\dfrac{x}{{27}}} \right)\]
x=\[\dfrac{{27}}{{27 \times 1000}}\]=${10}^{-3}$ \[ \times \]${10}^{6}$ ${ cm}^{3}$.
 = $10^3$ $cm^3$
= 1000 $cm^3$
Therefore, volume of tank=1000 $cm^3$
Hence, (i) height (actual) = 24 m
     (ii) volume of tank = 1000 $cm^3$

Note: Use 1:30 as model and actual dimension. Ratio 1:30 will be taken equal to ratio of height and volume accordingly. A ratio says how much of one thing there is compared to another thing.