I have tried to solve the following problem. When I perform the differentiation before supplying the given variables, I am left with two unknowns: dr/dt and dh/dt. When I try to remove a variable by supplying the radius as a constant before differentiation, I receive the wrong answer (it is exactly 3x too big). Several other problems later on give me the same trouble, so I am hoping that an understanding of this problem will enlighten me to the proper method to solve the others.
"A water tank is in the shape of a cone with vertical axis and vertex downward. The tank's radius is 3 ft. and the tank is 5 ft. high. At first the tank is full of water, but at time t = 0 (in seconds), a small hole at the vertex is opened, and the water begins to drain. When the height of water in the tank has dropped to 3 ft, the water is flowing out at 0.02 ft^3/s. At what rate, in feet per second, is the water level dropping then?"
I am working with a radius of 9/5 ft of the surface of the water.
Thank you in advance!