Posted by Anonymous on Tuesday, March 5, 2013 at 1:44pm.
A 3dimensional structure is obtained from rotating the parabola y=x^2 about the yaxis. 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.