Posted by **andy** on Thursday, July 18, 2013 at 12:14pm.

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?

- calculus -
**Steve**, Thursday, July 18, 2013 at 12:36pm
when the water depth is a, the volume is

v = ∫[0,a] π x^2 dy

= ∫[0,a] πy dy

= π/2 a^2

dv/dt = πa da/dt

when v=8π, a=4, so since dv/dt=2π,

2π = π(4) da/dt

da/dt = 1/2

1+2=3

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