Posted by **Anonymous** on Tuesday, March 5, 2013 at 1:44pm.

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 ab, where a and b are coprime positive integers. What is the value of a+b?

- math, calculus -
**Steve**, Tuesday, March 5, 2013 at 2:51pm
the volume of water when y=k is

∫[0,k] πx^2 dy

= ∫[0,k] πy dy

= π/2 k^2

So, at depth y,

v = π/2 y^2

when v=8π, y=4

dv/dt = πy dy/dt

2π = π(4) dy/dt

dy/dt = 1/2

You sure you want ab, and not a/b?

a+b = 1+2 = 3

- math, calculus -
**Anonymous**, Tuesday, March 5, 2013 at 4:36pm
Yes sorry, it's a/b.

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