Posted by **Alannah** on Sunday, December 16, 2012 at 5:29pm.

The base of a cone-shaped tank is a circle of radius 5 feet, and the vertex of the cone is 12 feet above the base. The tank is being filled at a rate of 3 cubic feet per minute. Find the rate of change of the depth of water in the tank when then depth is 7 feet.

- AP calculus -
**Steve**, Sunday, December 16, 2012 at 5:53pm
when the water is at depth x, the radius of the surface of the water is 5/12 (12-x)

so, the volume of the air space is 1/3 pi r^2 h

= 1/3 pi (5/12 (12-x))^2 (12-x)

= 25pi/432 (12-x)^3

the volume of water is thus the tank volume less the air space:

v = pi/3 * 25^2 * 12 - 25pi/432 (12-x)^3

= 100 pi - 25pi/432 (12-x)^3

dv/dt = 25/144 pi (12-x)^2 dx/dt

3 = 25/144pi * 25 dx/dt

dx/dt = 432/(625pi) = 0.22 ft/min

## Answer this Question

## Related Questions

- Calculus - A water tank is shaped like an inverted right circular cone with a ...
- Calculus - Water is draining at a rate of 2 cubic feet per minute from the ...
- AP CALCULUS!!! HELPP - related rates: the base of a pyramid-shaped tank is a ...
- AP CALCULUS!! HELPPP URGENT - related rates: the base of a pyramid-shaped tank ...
- CALCULUS - PLEASE HELP - Water is flowing at a rate of 50 cubic meters per ...
- calculus - A hollow cone has height 5 feet and base diameter 4 feet. The vertex...
- Calculus - Given a right circular cone, you put an upside-down cone inside it so...
- Math - A tank in the shape of a cone has a diameter of 8 feet and a height of 10...
- Calculus: Optimization - I have no idea how to approach this problem, if someone...
- Calculus - A water tank has a shape of an inverted circular cone with base ...