Posted by Rachel | Posted in Coffee and Accessories | Posted on 19-05-2009
Tags: coffee, coffee cone filter, coffee cone filter 4, coffee cone filter holder, coffee cone filter sizes, coffee cone filters 6, cone, filter, shop, wishlist
Does anyone know how to solve this problem?
Coffe is draining from a conical filter, diameter and height both 6 inches, into a cylindrical pot, diameter also 6 inches.
a) How fast is the level of coffee in the pot rising when coffee in the cone is 5 inches deep?
b)How fast is the level of coffee in the cone filter falling at that moment?
this is calculus 1 problem
For the filter the volume at any given height and radius is given by:
v = π*r^2*h/3
Since the height is 6 and the radius 3, no matter what level the coffee is the height will be twice the radius. So when the height of the coffee is 5 inches, the radius will be 2.5 inches.
a) For a pot, v = π*r^2*h
For the filter v = (π*h^3 / (3 * 4)) = ((π * h^3) / 12)
So dv/dt = (π h^2 / 4) dh/dt
We know that h = 5, dh/dt is unknown and we need it to find dv/dt
There isn’t enough information here. What I was going to do was substitute h and dh/dt to find out how fast the volume was changing in the filter and then use that speed of volume decrease to compute the speed of volume increase in the pot. But, as it is, without knowing at least one speed (dr/dt or dh/dt) for all I know it could be rushing through or going through a drop at a time.
Get the information as to dh/dt or dr/dt and email me and I’ll finish your problems. Otherwise this is as far as I can go.
.
I have a doctorate in math. I know what I’m talking about.
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