Question

A model of a tower block is made with a scale of 1 : 60. The volume of themodel is 36 000 cm3. Calculate the volume of the actual tower block in m3

Answer 1

Therefore, volume of actual tower = 2.16 m³

Explanation:

Scale of model to actual tower = 1:60

This means that the actual tower is larger than the model tower by a scale of 60 times

To calculate the volume of the actual tower, the following steps are used:

1 cm³ of model tower = 60 cm³ of actual tower

∴ 36,000 cm³ of model tower = 60 × 36,000 = 2,160,000 cm³

converting to m³

100 cm = 1 m

(100 cm)³ = (1 m)³

1,000,000 cm³ = 1 m³

∴ 1 cm³ =
`(1)/(1,000,000) m^(3)`

∴ 2,160,000 cm³ =
`(2,160,000)/(1,000,000) m^(3)` = 2.16 m³

Therefore, volume of actual tower = 2.16 m³

Answer 2

7776 m^3

Explanation:

The ratio of volumes is the cube of the scale factor. Here, the actual tower has dimensions 60 times those of the model, so the actual volume is ...

(36,000 cm^3)(60^3) = 7.776·10^9 cm^3

= 7.776·10^9(10^-2 m)^3

= 7776 m^3

The actual tower block has a volume of 7776 m^3.