Rotating Parabolas

Calculus Level 3

A 3-dimensional structure is obtained from rotating the parabola y=x2y=x^2 about the y-axis. Each second, 2π units32\pi \ \mbox{units}^3 of water is being poured into the structure from the top. When 8π units38\pi \ \mbox{units}^3 of water has been poured in the structure, the instantaneous change in water height level is ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+ba+b?

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