Help Neede On Related Rates (conical Cistern)

[marts237]

At a rate of 8ft^3/min, water is pouring into a conical cistern, if the height of a cistern is 12ft and the radius of it's circular opening is 6ft, how fast is the water level rising when the water is 4ft deep?

 

[HallsofIvy]

Having someone do the problem for you is not "help". What have you done? Do you know the equation for the volume of a cone in terms of height and radius? Do you see the relationship between height and radius of the water at any time in a cistern that is "12 ft high and radius 6 ft"? (draw a picture and think "similar triangles".)

Do you know how to go from a "static" formula (volume of cone) to a "rates" formula (how fast volume is changing)?