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January 5th, 2010

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Coffee is draining from from a conical filter into a cylindrical coffee pot at the rate of 10in^3/min. a.) How fast is the level in the pot rising when the coffee in the cone is 5in deep? b.) How fast is the level in the cone falling then?

The height of the cone is 6in and the diameter of the cone is 6in. The diameter of the pot in also 6 in. I have attempted this problem, but I know I am not approaching it right

V=pi/3*r^2*h

h/r=6/3
6r=3h
r=h/2

V=pi/3*(h/2)^2*h
V=pi/12h^3
DV/dt=3pi/4*h^2dh/dt

-10=pi/4*(5)^2dh/dt
-40/25pi=dh/dt, -8/5pi=dh/dt
The water level from the filter is falling at a rate 0f -8/5pi in/min

V=pir^2h
Dv/dt=pir^2dh/dt
10=pi(3)^2dh/dt
10/9pi=dh/dt

the water level in the pot is rising at the rate of 10/9pi in/min.

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