posted by andy .
A 3-dimensional structure is obtained from rotating the parabola y=x^2 about the y-axis. Each second, 2π units^3 of water is being poured into the structure from the top. When 8π units^3 of water has been poured in the structure, the instantaneous change in water height level is a/b, where a and b are coprime positive integers. What is the value of a+b?