The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3 inches more than the time, t. what will the volume, v, of the balloon be at t = 3 seconds? 36pi cubic inches 72pi cubic inches 288pi cubic inches 972pi cubic inches

The description of the problem is a bit ambiguous as "increasing at the rate of  3 inches more than the time" can be interpreted in many ways. Assuming the increase rate is the (3+t) per second and as it expands for 3 seconds, then the diameter of the sphere would be:
d= (3 + t)*t
d= 3t + t^2= 18

r= 1/2 d 
r= 1/2*18= 9

volume= 4/3 * pi * r^3
volume= 4/3 * pi * 9^3
volume= 4/3 * pi * 729= 972 pi cubic inches

The answer is b hope this