Question

The model of a building is constructed with a scale factor of 1 : 30.

1. If the height of the model is 80 cm, find the actual height of the building in metres.
2. 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 = 80 xx 1/30`

H = 2,400 cm

∴ H = 24 m

(ii)

`"Volume of model"/"Volume of tank" = (1/30)^3`

`"V"/(27) = (1)/(27,000)`

V = `27/(27,000)`

V = `(1)/(1,000)`

V = 0.001 m³

Convert to cm³ (optional but standard for models):

Since 1m³ = 1,000,000 cm³:

0.001 × 1,000,000 = 1,000 cm³

Hence, the volume of the tank on the model is 0.001 m³ (or 1,000 cm³).