The model of a 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 a tank at the top of the building is 27 m³, find the volume of the tank on the top of the model.

(i) Since, the model of the building is constructed with scale 1 : 30.

∴ k (Scale factor) = 30

Height of building = k × Height of model of the building = 30 × 80 = 2400 cm = $\dfrac{2400}{100}$ m = 24 m.

Hence, the height of building is 24 m.

(ii) Volume of the tank = k³ × (the volume of the model)

Given, volume of tank = 27 m³. Let volume of model be x m³. Putting value in above equation we get,

$\Rightarrow 27 = (30)^3 \times x \\[1em] \Rightarrow x = \dfrac{27}{30 \times 30 \times 30} \\[1em] \Rightarrow x = \dfrac{27}{27000} \\[1em] \Rightarrow x = \dfrac{1}{1000}.$

∴ x = $\dfrac{1}{1000} \text{ m}^3 = \dfrac{1}{1000} \times (100 \text{ cm})^3 = \dfrac{1000000}{1000} \text{ cm}^3 = 1000 \text{ cm}^3$.

Hence, the volume of the model is 1000 cm³.