The volume of air in a model car is #40cm^3# . A scale of 1:50 was used to create the model. What is the volume of air in the actual car?

Let's consider the computation as follows:

For example, if we have a line segment of length 1, and we want to scale it using the 1:50 ratio, the resultant scaled line segment will be 50. This is a very simple calculation to perform.

If you would like to convert to meters cubed:

Recognizing that the model and the actual car have comparable numbers is crucial.

Their volumes in comparable figures match the lengths' cube in ratio.

To find the volume of air in the actual car, we need to scale up the volume of the model car based on the given scale of 1:50.

Since the scale is 1:50, it means that every unit in the model represents 50 units in the actual car. Therefore, to find the volume of air in the actual car, we need to multiply the volume of air in the model car by $50^3$ (since volume is measured in three dimensions).

$\text{Volume of air in actual car} = \text{Volume of air in model car} \times (50^3)$

$\text{Volume of air in actual car} = 40 \, \text{cm}^3 \times (50^3)$

$\text{Volume of air in actual car} = 40 \, \text{cm}^3 \times 125,000$

$\text{Volume of air in actual car} = 5,000,000 \, \text{cm}^3$

So, the volume of air in the actual car is $5,000,000 \, \text{cm}^3$.