The answer I got was 17191, so I might have name a mistake, but this is how I done it.
The equation for the volume of a sphere is

The first balloon has a radius of 12 and when you use the equation the volume equals 7238.23cm³, and the second balloon has a radius of 18 and when you use the equation the volume equals 24429.02cm³. Subtract the smaller balloon from the larger balloon (24429.02 - 7238.23) and it equals 17190.79cm³ and when rounded gives you 17191cm³.