to completely cover a spherical ball, a ball company uses a total area of 36 square inches of material. what is the maximum volume the ball can have?

Area of a sphere is 4pr^2 and the volume of a sphere is (4pr^3)/3. 

You are told that A=36 so 

4pr^2=36 

pr^2=9 

r=(9/p)^(1/2) 

Using this r in the volume equation we see that... 

V=(4p/3)(9/p)^(3/2) 

V~20.31in^3