Rotating Parabolas

Calculus Level 3

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

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