Posted by **Liz** on Thursday, May 17, 2012 at 10:59pm.

A container is in the shape of an inverted right circular cone has a radius of 2 in at the top and a height of 6 in. At the instant when the water in the conatiner is 5 in deep, the surface level is falling at the rate of -.4 in/s. Find the rate at which the water is being drained.

- Calculus -
**Steve**, Thursday, May 17, 2012 at 11:31pm
when the water is at height x, by similar triangles, the radius r of the surface is given by

r/x = 2/6, so r = x/3

v = 1/3 pi (x/3)^2 * x

= pi/27 x^3

dv/dt = 2pi/27 x^2 dx/dt

-4 = 2pi/27 (25) dx/dt

dx/dt = -54/25pi = -.69 in/s

- Calculus - correction -
**Steve**, Thursday, May 17, 2012 at 11:34pm
dv/dt = 3pi/27 x^2 dx/dt

-4 = pi/9 (25) dx/dt

dx/dt = -36/25pi = -.46 in/s

## Answer this Question

## Related Questions

- Pure Maths - A container is in the shape of a right circular cone (inverted) ...
- calculus inverted cone - A container in the shape of an inverted cone has ...
- Calculus - A large container has the shape of a frustum of a cone with top ...
- Calculus - A large container has the shape of a frustum of a cone with top ...
- math - Suppose we pump water into an inverted right-circular cone tank at the ...
- calculus - A large container has the shape of a frustum of a cone with top ...
- Calculus - A vessel is in the shape of an inverted cone. The radius of the top ...
- Calculus - free body diagram - A water tank has the shape of an inverted right ...
- Calculus - A water tank has a shape of an inverted circular cone with base ...
- Calculus - A container in the form of a right circular cone (vertex down) has a...