Question

The volume of a machine is 27000 cm³. A model of the machine is made, the reduction factor being 2 : 15. Find the volume of the model.

Answer 1

Given:

• Volume of machine = 27000 cm³
• Reduction factor = 2 : 15

Reduction factor is the ratio of linear dimensions:

`"Model"/"Actual" = 2/15`

Volume ratio = `(2/15)^3`

∴ Volume ratio = `8/3375`

Now,

Volume of model = `27000 xx 8/3375`

= `27000/3375 xx 8`

= 8 × 8

∴ Volume of model = 64 cm³