Since the constant rate is not given in the problem, I don't think you can be exact. However, we know that the volume of a sphere (V)= 4pi(r3)/3. Let's say that the constant is 1 cubic inch per second (just for simplicity). At time (t)=0, the volume is going to be 0. Therefore, if we plug in 0 for V and solve for r, we get 0. If you do the same for t=1, 2, and 3, you get a graph that looks somewhat like a square root function.
Another way to look at it is this:
V= 4pi(r3)/3
V is also equal to t times the constant rate ©. V=tc
Therefore, 4pi(r3)/3=tc
Make up a number for the constant and replace c with that number.
Substitute different values for time and solve for r.