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.
Answer This Question
Related Questions
 calculus  A 3dimensional structure is obtained from rotating the parabola y=x^...
 calculus  A 3dimensional structure is obtained from rotating the parabola y=x^...
 Calculus  Rates of Change  A water tank has a shape of an inverted cone with a...
 Calculus  A cylindrical jar of radius 5 cm contains water to a depth of 8 cm. ...
 Calculus @ Henry  I worked some on this earlier, and botched it a bit, so here ...
 Math  If a hemispherical bowl of radius 6cm contains water to a depth of h cm, ...
 Math integrals  What is the indefinite integral of ∫ [sin (π/x)]/ x^...
 Calculus  How do I find the critical values? y= 4/x + tan(πx/8) What I ...
 Math  Evaluate *Note  We have to find the exact value of these. That I know to...
 Math, please help  Which of the following are trigonometric identities? (Can be...
More Related Questions