Coffee is draining from a conical filter into a cylindrical coffee pot at a rate of 16? 3 / min. Both the conical filter and cylindrical coffee pot are 8 inches across and 8 inches deep. (a) How fast is the level in the coffee pot rising when the coffee in the cone is 6 inches deep?

dh/dt = 0.318 in/min

Explanation:

Given that

dV/dt = 16 in³/min

Volume of the cylindrical pot

V = πr²h

r=radius

h=height

Given that

d=h = 8 in

h = 2 r

radius of cylinder r = 4 in

V = πr²h

V = 16πh

By differentiating with respect to time t

dV/dt = 16π dh/dt

Given that

dV/dt = 16 in³/min

16 in³/min = 16π dh/dt

dh/dt = 0.318 in/min