# 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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