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

## Answer This Question

## Related Questions

- calculus - A 3-dimensional structure is obtained from rotating the parabola y=x^...
- math, calculus - A 3-dimensional structure is obtained from rotating the ...
- 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 ...
- Calculus - The volume of the 3-dimensional structure formed by rotating the ...
- Calculus - The volume of the 3-dimensional structure formed by rotating the ...
- calculus - The volume of the 3-dimensional structure formed by rotating the ...
- calculus - The volume of the 3-dimensional structure formed by rotating the ...
- Calculus - How do I find the critical values? y= 4/x + tan(πx/8) What I ...

More Related Questions