Simple explanation: when you scale all of the sides of a prism, the volume changes by the scale factor CUBED (it's distributing to all of the sides)
Just put in your calculator:
[tex]\frac{390}{18^3} - \frac{390}{24^3}[/tex]
(We know that 18*18*18 is going to be larger than 24*24*24, and when you divide something by a larger number, it's going to be less, so the 1:24 model is going to have a lesser volume)
and you should get an answer about equal to
[tex]\boxed{0.04\ in^3}[/tex]
(I'm pretty sure your teacher doesn't want a fraction, because the exact answer is [tex]\frac{2405}{62208}[/tex])
