Posted by **Helga** on Monday, November 21, 2011 at 6:55am.

A container in the form of a right circular cone of height 16 cm and base radius 4 cm is held vertex downward and filled with liquid. If the liquid leaks out from the vertex at a rate of 4 cm^3/s, find the rate of change of the depth of the liquid in the cone when half of the liquid has leaked out.

- Calculus -
**Steve**, Monday, November 21, 2011 at 9:28am
When the water is x cm deep, and the surface is a circle of radius r

r/x = 4/16

r = x/4

v = pi/3 r^2 x = pi/3 x^2/16 x = pi/48 x^3

Now, what is x when half the liquid is gone?

pi/3 r^2 x = pi/3 * 16 * 16 / 2

x^3/4 = 128

x^3 = 2^11 = 2^9 * 4

x = 8 cbrt(4)

dv/dt = pi/16 x^2 dx/dt

4 = pi/16 * 64 cbrt(16) dx/dt

dx/dt = 64/pi / (128cbrt(2)) = .126 cm/s

Better check the details...

## Answer this Question

## Related Questions

- geometry math - There is an upside-down cone that is 12m high and has a circular...
- Calculus Practice Problems - A filter filled with liquid is in the shape of a ...
- Calculus - Given a right circular cone, you put an upside-down cone inside it so...
- math - Two right circular cone, one upside down in the other. The two bases are ...
- Calculus: Optimization - I have no idea how to approach this problem, if someone...
- math - A cone shaped container with its vertex at the top and its circular base ...
- calculus inverted cone - A container in the shape of an inverted cone has ...
- Physics (cone in water) buoyancy - h ttps ://s.yimg . com /hd/ answers /i /...
- Calculus - A container in the form of a right circular cone (vertex down) has a...
- Pure Maths - A container is in the shape of a right circular cone (inverted) ...

More Related Questions