Question

The model of a building is constructed with 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.

Answer 1

(i)  `"Height of model"/"Height of actual building" = (1)/(30)`
`(80)/"H" = (1)/(30)`
⇒ H = 2,400 cm = 24 m.
(ii) `"Volume of model"/"Volume of tank" = (1/30)^3`
`"V"/(27) = (1)/(27,000)`
V = `(1)/(1,000)"m"^3`
= 1,000 cm³.