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
