Aball made out of a special material is inflated such that its diameter changes from 12inches to 15 inches. what is the approximate change in the volume of the ball?

A ball should give you the idea that we’re dealing with spheres. The volume of a sphere is:

V = (4/3) • π • r^3

The initial radius is 6 inches (radius is half of diameter)
Plug in to get its volume:

V = (4/3) • π • (6)^3

V is about 904.7787 in^3

Now do the same for the enlarged sphere, with radius 7.5 inches

V = (4/3) • π • (7.5)^3

V is about 1767.1459 in^3

To find the change, get the difference between the two volumes:

(New Volume) - (Old Volume)

1767.1459 - 904.7787

The change is around 862.3672 in^3