Question

Coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 12 in^3/min.
*height of cone: 6 in
*Diameter of cone: 6 inch
*diameter of cylinder: 6 in
Volume of Cylinder: V= pir^2h
Volume of Cone: V= (1/3)pir^2h

a) how fast is the level in the pot rising when the coffee in the cone is 4 in deep?
b) how fast is the level in the cone falling at that moment?

Am I supposed to take the derivative of both formula? Please help me as I am somewhat confused on how to get started.

Answer 1

Okay, let's start, haven't done a problem like this in a while...

First off, you need to describe the radius of the cone as a function of the heigh

Answer 2

height*