Answer:
- width: 2 : 15
- volume: 8 : 3375
- surface area: 4 : 225
Explanation:
Given a model has a scale factor of 2:15 with respect to the original car, you want to know the ratios of model : original for width, volume, and surface area.
Ratios
The scale factor is the ratio of linear dimensions, such as width. This means the ratio of widths will be 2:15, the same as the scale factor.
Areas have units of the square of a linear dimension. Hence the ratio of areas is the square of the ratio of linear dimensions, the square of the scale factor. The ratio of surface areas will be 2²:15² = 4:225.
Volumes have units of the cube of a linear dimension. Hence the ratio of volumes is the cube of the ratio of linear dimensions, the cube of the scale factor. The ratio of volumes will be 2³:15³ = 8:3375.
The model : original ratios are ...
- width: 2 : 15
- volume: 8 : 3375
- surface area: 4 : 225
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