Answer: 18 cm
==============================================
Step-by-step explanation:
The volume of a sphere is found by this formula
V = (4/3)*pi*r^3
We are given the volume is V = 972pi and we need to find r
Plug in that value for V and solve for r
V = (4/3)*pi*r^3
972pi = (4/3)*pi*r^3
972 = (4/3)*r^3 ... the pi's cancel out (divide both sides by pi)
3*972 = 4r^3 ... multiply both sides by 3
2916 = 4r^3
4r^3 = 2916
r^3 = 2916/4 ... divide both sides by 4
r^3 = 729
r = (729)^(1/3) ... apply the cube root to both sides
r = 9
The radius is 9, so the diameter is
d = 2*r = 2*9 = 18 cm