Posted by Rachel | Posted in Coffee and Accessories | Posted on 12-08-2008
Tags: cone coffee filters 6, recipes
help with change of rate calculus problem?
Coffee is draining form a conical filter into a cylindrical coffeepot at the rate of 10 in^3/min.
a. how fast is the level in the pot rising when the coffee in the cone is 5 in deep?
b. how fast is the level in the cone falling then?
*the height and diameter of the cone are both 6 inches
*the diameter of the coffee pot is 6 inches
a.
let h be the height of the coffeepot.
dh/dt = dV/dt x dh/dV
V = 6πh
dV/dh = 6π
dh/dV = 1/(6π)
dh/dt = 10 x 1/(6π)
dh/dt = 0.53 in/min
b.
let d be the height of the conical filter.
dd/dt = dV/dt x dd/dV
V = ⅓πr²d
r = ½d
V = ⅓π(½d)²d
V = 1/12πd³
dV/dd = ¼πd²
dd/dV = 4/(πd²)
dd/dt = 10 x 4/(πd²)
dd/dt = 10 x 4/(π(5)²)
dd/dt = 0.51 in/min
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